BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Matthias Röger (Technische Universität Dortmund) DTSTART:20200421T150000Z DTEND:20200421T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/1 DESCRIPTION:Title: An obstacle type problem as a limit of a model for cell polariza tion\nby Matthias Röger (Technische Universität Dortmund) as part of Lisbon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Goldman (Laboratoire Jacques-Louis Lions and Université P aris 7) DTSTART:20200428T150000Z DTEND:20200428T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/2 DESCRIPTION:Title: On an old conjecture of Almgren\nby Michael Goldman (Laborat oire Jacques-Louis Lions and Université Paris 7) as part of Lisbon webina r in analysis and differential equations\n\n\nAbstract\nIn this talk I wil l give an overview on the few results available on the conjecture of Almgr en regarding the convexity of drops subject to the action of an external p otential. In particular I will present recent progress in this direction o btained with G. De Philippis on their connectedness. Together with an olde r result of McCann\, this answers positively the conjecture in dimension t wo. The proof is inspired by the two-point function technique introduced b y B. Andrews and is reminiscent of the doubling of variables trick in the context of viscosity solutions.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Filippo Santambrogio\, (Université Claude Bernard - Lyon 1) DTSTART:20200505T150000Z DTEND:20200505T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/3 DESCRIPTION:Title: Optimal transport methods for the regularity of 2D functions of least gradient\nby Filippo Santambrogio\, (Université Claude Bernard - Lyon 1) as part of Lisbon webinar in analysis and differential equations \n\n\nAbstract\nThe least gradient problem (minimizing the BV norm with gi ven boundary data)\, motivated by both image processing applications and c onnections with minimal surfaces\, is known to be equivalent\, in the plan e\, to the Beckmann minimal-flow problem (an alternative formulation of th e $L^1$ Monge-Kantorovich optimal transport problem) with source and targe t measures located on the boundary of the domain. Hence\, Sobolev regulari ty of functions of least gradient is equivalent in this setting to $L^p$ b ounds on the solution of the Beckmann problem (i.e. on what is called the transport density) and can be attacked with techniques which are now stand ard in optimal transport. From the transport point of view\, the novelty o f the estimates that I will present\, coming from a joint paper with S. Dw eik\, lies in the fact they are obtained for transport between measures wh ich are concentrated on the boundary. From the BV point of view\, a new re sult is the $W^{1\,p}$ regularity of the least gradient function whenever the boundary datum is $W^{1\,p}$ as a 1D function: moreover\, the optimal transport framework is strong enough to deal with arbitrary strictly conve x norms instead of the Euclidean one with almost no effort.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Diogo Oliveira e Silva (University of Birmingham) DTSTART:20200512T153000Z DTEND:20200512T163000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/4 DESCRIPTION:Title: Global maximizers for spherical restriction\nby Diogo Olivei ra e Silva (University of Birmingham) as part of Lisbon webinar in analysi s and differential equations\n\n\nAbstract\nWe prove that constant functio ns are the unique real-valued maximizers for all $L^2-L^{2n}$ adjoint Four ier restriction inequalities on the unit sphere $\\mathbb{S}^{d-1}\\subset \\mathbb{R}^d$\, $d\\in\\{3\,4\,5\,6\,7\\}$\, where $n\\geq 3$ is an integ er. The proof uses tools from probability theory\, Lie theory\, functional analysis\, and the theory of special functions. It also relies on general solutions of the underlying Euler--Lagrange equation being smooth\, a fac t of independent interest which we discuss. We further show that complex-v alued maximizers coincide with nonnegative maximizers multiplied by the ch aracter $e^{i\\xi\\cdot\\omega}$\, for some $\\xi$\, thereby extending pre vious work of Christ & Shao (2012) to arbitrary dimensions $d\\geq 2$ and general even exponents. This talk is based on results obtained with René Quilodrán.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Bernold Fiedler (Institute of Mathematics\, Freie Universität Ber lin) DTSTART:20200519T150000Z DTEND:20200519T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/5 DESCRIPTION:Title: Sturm meanders: global attractors\, Temperley-Lieb algebras\, an d black holes\nby Bernold Fiedler (Institute of Mathematics\, Freie Un iversität Berlin) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nFusco and Rocha studied Neumann boundary value pr oblems for scalar ODEs of second order via a shooting approach. They intro duced the notion of what we now call Sturm permutations. These permutation s relate\, on the one hand\, to a special class of meandering curves as in troduced by Arnol’d in a singularity theory context. On the other hand\, they became central in the study of global attractors of nonlinear parabo lic partial differential equations of Sturm type.\n\nWe discuss relations of Sturm meanders with further areas: the multiplicative and trace structu re in Temperley-Lieb algebras\, discrete versions of Cartesian billiards\, and the problem of constructing initial conditions for black hole dynamic s which satisfy the Einstein constraints. We also risk a brief glimpse at the long and meandric history of meander patterns themselves.\n\nWe report on joint work with Pablo Castañeda\, Juliette Hell\, Carlos Rocha\, and Brian Smith. See also http://dynamics.mi.fu-berlin.de/\n\nFor further mate rial we recommend the beautifully illustrated book “Meanders” by Anna Karnauhova\, de Gruyter 2017.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Luis Vega (BCAM) DTSTART:20200526T150000Z DTEND:20200526T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/6 DESCRIPTION:Title: The Vortex Filament Equation\, the Talbot effect\, and non-circu lar jets.\nby Luis Vega (BCAM) as part of Lisbon webinar in analysis a nd differential equations\n\n\nAbstract\nWe will propose the vortex filame nt equation as a possible toy model for turbulence\, in particular because of its striking similarity to the dynamics of non-circular jets. This sim ilarity implies the existence of some type of Talbot effect due to the int eraction of non-linear waves that propagate along the filament. Another co nsequence of this interaction is the existence of a new class of multi-fra ctal sets that can be seen as a generalization of the graph of Riemann’s non-differentiable function. Theoretical and numerical arguments about th e transfer of energy will be also given. This a joint work with V. Banica and F. de la Hoz.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Colombo (EPFL) DTSTART:20200602T150000Z DTEND:20200602T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/7 DESCRIPTION:Title: Nonunique characteristic curves of Sobolev vector fields\nby Maria Colombo (EPFL) as part of Lisbon webinar in analysis and differenti al equations\n\n\nAbstract\nGiven a vector field in $\\mathbb{R}^d$\, the classical Cauchy-Lipschitz theorem shows existence and uniqueness of its f low provided the vector field is sufficiently smooth\; this\, in turn\, tr anslates in existence and uniqueness results for the transport equation. I n 1989\, Di Perna and Lions proved that Sobolev regularity for vector fiel ds\, with bounded divergence and a growth assumption\, is sufficient to es tablish existence\, uniqueness and stability of a generalized notion of fl ow\, consisting of a suitable selection among the trajectories of the asso ciated ODE. A long-standing open question is whether the uniqueness of the regular Lagrangian flow is a corollaryof the uniqueness of the trajectory of the ODE for a.e. initial datum. In this talk we give an overview of th e topic and we provide a negative answer to this question. To show this re sult we exploit the connection with the transport equation\, based on Ambr osio’s superposition principle\, and a new ill-posedness result for posi tive solutions of the continuity equation.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucio Boccardo (Università di Roma La Sapienza) DTSTART:20200609T150000Z DTEND:20200609T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/8 DESCRIPTION:Title: Recent developments on Dirichlet problems with singular convecti on/drift terms\nby Lucio Boccardo (Università di Roma La Sapienza) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstra ct\nPlease check https://wade.ulisboa.pt/seminars?id=5797\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Riccardo Adami (Politecnico di Torino) DTSTART:20200616T150000Z DTEND:20200616T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/9 DESCRIPTION:Title: Ground states of the Nonlinear Schroedinger Equation on Graphs: an overview\nby Riccardo Adami (Politecnico di Torino) as part of Lisb on webinar in analysis and differential equations\n\n\nAbstract\nDriven by physical and technological applications\, during the last five years the study of nonlinear evolution on branched structures (graphs\, networks) ha s undergone a fast development. We review on the main achievements and on the open problems. This is a joint project with several people\, among whi ch Simone Dovetta\, Enrico Serra\, Lorenzo Tentarelli\, and Paolo Tilli.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Tatsuya Miura (Tokyo Institute of Technology) DTSTART:20200623T100000Z DTEND:20200623T110000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/10 DESCRIPTION:Title: On the isoperimetric inequality and surface diffusion flow for multiply winding curves\nby Tatsuya Miura (Tokyo Institute of Technolo gy) as part of Lisbon webinar in analysis and differential equations\n\n\n Abstract\nIn this talk we discuss dynamical stability of multiply covered circles under the surface diffusion flow. To this end we first establish a general form of the isoperimetric inequality for immersed closed curves u nder rotational symmetry\, which would be of independent interest. We then apply it to obtaining a certain class of rotationally symmetric initial c urves from which solutions to the surface diffusion flow exist globally-in -time and converge to multiply covered circles. This talk is based on a jo int work with Shinya Okabe at Tohoku University.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Barbara Brandolini (Università Degli Studi di Napoli Federico II) DTSTART:20200630T150000Z DTEND:20200630T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/11 DESCRIPTION:Title: Sharp lower bounds for Neumann eigenvalues.\nby Barbara Bra ndolini (Università Degli Studi di Napoli Federico II) as part of Lisbon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Elvira Zappale (Università Degli Studi di Salerno) DTSTART:20200709T150000Z DTEND:20200709T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/12 DESCRIPTION:Title: Optimal design problems\nby Elvira Zappale (Università Deg li Studi di Salerno) as part of Lisbon webinar in analysis and differentia l equations\n\n\nAbstract\nI will present several integral representation results for certain functionals arising in the context of optimal design a nd damage models\, in presence of a perimeter penalization term. I will co nsider several frameworks\, and I will also discuss the case with non-stan dard growth conditions.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Exner (Doppler Institute for Mathematical Physics and Applie d Mathematics\, Prague) DTSTART:20200714T150000Z DTEND:20200714T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/13 DESCRIPTION:Title: Vertex coupling and spectra of periodic quantum graphs\nby Pavel Exner (Doppler Institute for Mathematical Physics and Applied Mathem atics\, Prague) as part of Lisbon webinar in analysis and differential equ ations\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Baptiste Casteras (Universidade de Lisboa) DTSTART:20201022T133000Z DTEND:20201022T143000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/14 DESCRIPTION:Title: Standing wave and travelling wave solutions for a fourth order Schrödinger equation\nby Jean-Baptiste Casteras (Universidade de Lisb oa) as part of Lisbon webinar in analysis and differential equations\n\n\n Abstract\nIn this talk\, we will be interested in standing wave solutions to a fourth order nonlinear Schrödinger equation having second and fourth order dispersion terms. This kind of equation naturally appears in nonlin ear optics. In a first time\, we will establish the existence of ground-st ate and renormalized solutions. We will then be interested in their qualit ative properties\, in particular their stability.\n\nJoint works with Deni s Bonheure\, Ederson Moreira Dos Santos\, Tianxiang Gou\, Louis Jeanjean a nd Robson Nascimento.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Piotr Chruściel & Lorenzo Mazzieri (University of Vienna / Univer sità di Trento) DTSTART:20201029T133000Z DTEND:20201029T143000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/15 DESCRIPTION:Title: Static vacuum black holes and Lambda\nby Piotr Chruściel & Lorenzo Mazzieri (University of Vienna / Università di Trento) as part o f Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe will review the status of the uniqueness theory of static vacuum black hol es\, with or without a cosmological constant $\\Lambda$\, and we will outl ine the proof of a uniqueness theorem with $\\Lambda>0$\, proved jointly i n collaboration with Stefano Borghini.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Rainer Mandel (Karlsruhe Institute of Technology) DTSTART:20201112T143000Z DTEND:20201112T153000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/16 DESCRIPTION:Title: New dual variational methods for Nonlinear Helmholtz Equations and polychromatic solutions of Nonlinear wave equations\nby Rainer Man del (Karlsruhe Institute of Technology) as part of Lisbon webinar in analy sis and differential equations\n\n\nAbstract\nIn the first part of my talk \, I present the classical dual variational method in the context of Nonli near Helmholtz equations that describe monochromatic waves in nonlinear ma terials. Afterwards\, I discuss two recent generalizations of the method. The first deals with an extension to Nonlinear Helmholtz equations with si gn-changing nonlinearities. For these problems we construct solutions that have infinite Morse-Index in the dual variational formulation. The second generalization concerns dual variational methods for the construction of breathers\, i.e.\, polychromatic\, spatially localized and time-periodic s olutions of nonlinear wave equations.\n\nThe results were obtained in coll aboration with D. Scheider and T. Yesil.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Youcef Mammeri (Université de Picardie Jules Verne) DTSTART:20201203T143000Z DTEND:20201203T153000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/17 DESCRIPTION:Title: A SIR-type model with diffusion to describe the spatial spread of Covid-19\nby Youcef Mammeri (Université de Picardie Jules Verne) a s part of Lisbon webinar in analysis and differential equations\n\n\nAbstr act\nWe all have to deal with the coronavirus epidemic. Many strategies ha ve been put in place to try to contain the disease\, with varying success. \nI will present an SIR-type mathematical model to predict the state of th e epidemic. The effect of distancing\, isolation of exposed individuals an d treatment of symptoms will be compared. \nI will begin with a simple exp lanation of SIR models\, then discuss a PDE model and its resolution.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Wladimir Neves (Universidade Federal do Rio de Janeiro) DTSTART:20201105T143000Z DTEND:20201105T153000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/18 DESCRIPTION:Title: Homogenization of Schrödinger equations. Extended Effective Ma ss Theorems for non-crystalline matter.\nby Wladimir Neves (Universid ade Federal do Rio de Janeiro) as part of Lisbon webinar in analysis and d ifferential equations\n\n\nAbstract\nIn this talk\, we study the homogeniz ation of the Schrödinger equation beyond the periodic setting. More preci sely\, rigorous derivation of the effective \nmass theorems in solid state physics for non-crystalline \nmaterials are obtained.\n\nThis is a joint work with Vernny Ccajma and Jean Silva.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Hynek Kovařík (Università degli studi di Brescia) DTSTART:20201116T143000Z DTEND:20201116T153000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/19 DESCRIPTION:Title: Absence of positive eigenvalues of magnetic Schroedinger operat ors\nby Hynek Kovařík (Università degli studi di Brescia) as part o f Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe study sufficient conditions for the absence of positive eigenvalues of mag netic Schroedinger operators in $\\mathbb{R}^n$. In our main result we pro ve the absence of eigenvalues above certain threshold energy which depends explicitly on the magnetic and electric field. A comparison with the exam ples of Miller-Simon shows that our result is sharp as far as the decay of the magnetic field is concerned.\n\nThe talk is based on a joint work wit h Silvana Avramska-Lukarska and Dirk Hundertmark.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Caroccia (Università degli studi di Roma Tor Vergata) DTSTART:20201126T143000Z DTEND:20201126T153000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/20 DESCRIPTION:Title: Contact surface of Cheeger sets\nby Marco Caroccia (Univers ità degli studi di Roma Tor Vergata) as part of Lisbon webinar in analysi s and differential equations\n\n\nAbstract\nGeometrical properties of Chee ger sets have been deeply studied by many authors since their introduction \, as a way of bounding from below the first Dirichlet (p)-Laplacian eigen vualue. They represents the first eigenfunction of the Dirichlet (1)-Lapla cian of a domain. In this talk we will introduce a recent property\, studi ed in collaboration with Simone Ciani\, concerning their contact surface w ith the ambient space. In particular we will show that the contact surface cannot be too small\, with a lower bound on the dimension strictly relate d to the regularity of the ambient space. The talk will focus on the intro duction of the problem and with a brief explanation of its connection with the Dirichlet (p)-Laplacian eigenvalue problem. Then a brief sketch of th e proof is given. Functional to the whole argument is the notion of remova ble singularity\, as a tool for extending solutions of pdes under some reg ularity constraint.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Qiao Huang (GFM\, University of Lisbon) DTSTART:20201210T143000Z DTEND:20201210T153000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/21 DESCRIPTION:Title: Stochastic Cucker-Smale model: collision-avoidance and flocking \nby Qiao Huang (GFM\, University of Lisbon) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nIn this talk\, we c onsider the Cucker-Smale flocking model involving both singularity and noi se. We first show the local strong well-posedness for the system\, in whic h the communication weight is locally Lipschitz beyond the origin. Then\, for the special case that the communication weight has a strong singularit y at the origin\, we establish the global well-posedness by showing the fi nite time collision-avoidance. Finally\, we study the large time behavior of the system when the communication weight is of zero lower bound. The co nditional flocking emerges for the case of constant noise intensity\, whil e the unconditional flocking emerges for various time-varying intensities and long-range communications.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Francois Babadjian (Université Paris Saclay) DTSTART:20201126T133000Z DTEND:20201126T143000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/22 DESCRIPTION:Title: Concentration versus oscillation effects in brittle damage\ nby Jean-Francois Babadjian (Université Paris Saclay) as part of Lisbon w ebinar in analysis and differential equations\n\n\nAbstract\nThis talk is concerned with the asymptotic analysis of a variational model of brittle d amage\, when the damaged zone concentrates into a set of zero Lebesgue mea sure\, and\, at the same time\, the stiffness of the damaged material beco mes arbitrarily small. In a particular non-trivial regime\, concentration leads to a limit energy with linear growth as typically encountered in per fect plasticity. While the singular part of the limit energy can be easily described\, the identification of the bulk part of the limit energy requi res a subtler analysis of the interplay between concentration and oscillat ion properties of the displacements.\nThis is a joint work with F. Iurlano and F. Rindler.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Svetlana Roudenko (Florida International University) DTSTART:20201217T143000Z DTEND:20201217T153000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/23 DESCRIPTION:Title: Zakharov-Kuznetsov equation: toward soliton resolution\nby Svetlana Roudenko (Florida International University) as part of Lisbon web inar in analysis and differential equations\n\n\nAbstract\nWe consider Zak harov-Kuznetsov (ZK) equation\, which is a higher-dimensional version of t he Korteweg-de Vries (KdV) equation\, and investigate the dynamics of solu tions\, especially questions about the soliton stability. We first discuss the situation in two dimensions\, in particular\, the instability of soli tons in the 2d cubic (critical) ZK equation\, which leads to blow-up. Then we consider the 3d quadratic ZK equation\, originally introduced by Zakha rov and Kuznetsov in early 1970's\, and discuss the asymptotic stability o f solitons. We will also show numerical findings on the formation of solit ons and radiation in this equation. This talk will be based on joint works with L.G. Farah\, J. Holmer\, C. Klein\, N. Stoilov\, K. Yang.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Nilima Nigam (Simon Fraser University) DTSTART:20210107T163000Z DTEND:20210107T173000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/24 DESCRIPTION:Title: Boundary integral strategies for the Steklov eigenproblem\n by Nilima Nigam (Simon Fraser University) as part of Lisbon webinar in ana lysis and differential equations\n\n\nAbstract\nIn Steklov eigenproblems f or elliptic operators\, the spectral parameter links boundary traces of ei genfunctions to traces of the Neumann data. It is natural\, therefore\, to reformulate such eigenproblems in terms of boundary integral operators\, which allow for nonsmooth boundaries. In this talk we describe such strate gies in the context of Steklov problems for the Laplacian as well as the H elmholtz operator\, and their use in studying questions arising in spectra l geometry.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Serena Dipierro & Enrico Valdinoci (University of Western Australi a) DTSTART:20210114T100000Z DTEND:20210114T120000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/25 DESCRIPTION:Title: Nonlocal Minimal Surfaces: interior regularity\, boundary behav ior and stickiness phenomena\nby Serena Dipierro & Enrico Valdinoci (U niversity of Western Australia) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nSurfaces which minimize a nonlocal p erimeter functional exhibit quite different behaviors than the ones minimi zing the classical perimeter. We will investigate some structural properti es of nonlocal minimal surfaces both in the interior of a given domain and in the vicinity of its boundary.\nAmong these peculiar features\, an inte resting property\, which is also in contrast with the pattern produced by the solutions of linear equations\, is given by the capacity\, and the str ong tendency\, of adhering at the boundary. We will also discuss this phen omenon and present some recent results.\n\n(these are two consecutive talk s: Part I is given by Serena Dipierro\, Part II by Enrico Valdinoci)\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles Collot (Cergy Paris Université) DTSTART:20210121T140000Z DTEND:20210121T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/26 DESCRIPTION:Title: On the stability of equilibria for infinitely many particles\nby Charles Collot (Cergy Paris Université) as part of Lisbon webinar i n analysis and differential equations\n\n\nAbstract\nWe study the evolutio n of a system of particles. Instead of the usual Hartree equation for dens ity matrices\, we consider the following equivalent model\, proposed by de Suzzoni\, of a Hartree type equation but for a random field:$$iX_t=-\\Del ta X +(w*\\mathbb E(|X|^2))X.$$Above\, $X:[0\,T]\\times \\mathbb R^d\\time s \\Omega$ is a time-dependent random field\, $w$ a pair interaction poten tial\, $*$ the convolution product and $\\mathbb E$ the expectation. This equation admits equilibria which are random Gaussian fields whose laws are invariant by time and space translations. They are hence not localised an d represent an infinite number of particles. We give a stability result un der certain hypotheses\, by showing that small perturbations scatter as $t \\rightarrow \\pm \\infty$ to linear waves. This is joint work with de Suz zoni.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Enrico Serra (Politecnico di Torino) DTSTART:20210128T140000Z DTEND:20210128T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/27 DESCRIPTION:Title: NLS ground states on metric trees: existence results and open q uestions\nby Enrico Serra (Politecnico di Torino) as part of Lisbon we binar in analysis and differential equations\n\n\nAbstract\nWe consider th e minimization of the NLS energy on a metric tree\, either rooted or unroo ted\, subject to a mass constraint. With respect to the same problem on ot her types of metric graphs\, several new features appear\, such as the exi stence of minimizers with positive energy\, and the emergence of unexpecte d threshold phenomena. We also study the problem with a radial symmetry co nstraint that is in principle different from the free problem due to the f ailure of the Polya-Szego inequality for radial rearrangements. A key role is played by a new Poincaré inequality with remainder.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Boyan Sirakov (PUC - Rio) DTSTART:20210225T140000Z DTEND:20210225T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/28 DESCRIPTION:Title: The Vázquez maximum principle and the Landis conjecture for el liptic PDE with unbounded coefficients\nby Boyan Sirakov (PUC - Rio) a s part of Lisbon webinar in analysis and differential equations\n\n\nAbstr act\nIn this joint work with P. Souplet we develop a new\, unified approac h to the following two classical questions on elliptic PDE:\n(i) the stron g maximum principle for equations with non-Lipschitz nonlinearities\; and\ n(ii) the at most exponential decay of solutions in the whole space or ext erior domains.\n\nOur results apply to divergence and nondivergence operat ors with locally unbounded lower-order coefficients\, in a number of situa tions where all previous results required bounded ingredients. Our approac h\, which allows for relatively simple and short proofs\, is based on a (w eak) Harnack inequality with optimal dependence of the constants in the lo wer-order terms of the equation and the size of the domain\, which we esta blish.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Yvan Martel (École Polytechnique) DTSTART:20210204T140000Z DTEND:20210204T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/29 DESCRIPTION:Title: On the asymptotic stability of kinks for (1+1)-scalar field mod els\nby Yvan Martel (École Polytechnique) as part of Lisbon webinar i n analysis and differential equations\n\n\nAbstract\n

The talk concerns stability properties of kinks for (1+1)-dimensional nonlinear scalar field models of the form
\\[\\partial_t^2 \\phi - \\partial_x^2 \\phi + W' (\\phi) = 0 \\quad (t\,x) \\in {\\bf R}\\times {\\bf R}.\\]
We establ ish a simple and explicit sufficient condition on the potential $W$ for th e asymptotic stability of a given moving or standing kink.
We present applications of the criterion to some models of the Physics literature.

Work in collaboration with Michał Kowalczyk\, Claudio Muñoz and Han ne Van Den Bosch

https:// arxiv.org/abs/2008.01276

See also the related work with Michał Kowalczyk and Claudio Muñoz

https://arxiv.org/abs/1903.12460

\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Bozhidar Velichkov (Università di Pisa) DTSTART:20210304T140000Z DTEND:20210304T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/30 DESCRIPTION:Title: Vectorial free boundary problems\nby Bozhidar Velichkov (Un iversità di Pisa) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nThe vectorial Bernoulli problem is a variational free boundary problem involving the Dirichlet energy of a vector-valued fu nction and the measure of its support. It is the vectorial counterpart of the classical one-phase Bernoulli problem\, which was first studied by Alt and Caffarelli in 1981.\n\nIn this talk\, we will discuss some results on the regularity of the vectorial free boundaries obtained in the last year s by Caffarelli-Shahgholian-Yeressian\, Kriventsov-Lin\, Mazzoleni-Terraci ni-V.\, and Spolaor-V.. Finally\, we will present some new results on the rectifiability of the singular set obtained in collaboration with Guido De Philippis\, Max Engelstein and Luca Spolaor.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Dario Mazzoleni (Università di Pavia) DTSTART:20210304T150000Z DTEND:20210304T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/31 DESCRIPTION:Title: Regularity of the optimal sets for the second Dirichlet eigenva lue\nby Dario Mazzoleni (Università di Pavia) as part of Lisbon webin ar in analysis and differential equations\n\n\nAbstract\nFirst of all\, we recall the basic notions and results concerning shape optimization proble ms for the eigenvalues of the Dirichlet Laplacian.\nThen we focus on the s tudy of the regularity of the optimal shapes and on the link with the regu larity of related free boundary problems.\n\nThe main topic of the talk is the regularity of the optimal sets for a "degenerate'" functional\, namel y the second Dirichlet eigenvalue in a box. Given $D\\subset \\mathbb{R}^d $ an open and bounded set of class $C^{1\,1}$\, we consider the following shape optimization problem\, for $\\Lambda>0$\,\\begin{equation}\\label{eq :main}\\min{\\Big\\{\\lambda_2(A)+\\Lambda |A| : A\\subset D\,\\text{ open }\\Big\\}}\,\\end{equation}where $\\lambda_2(A)$ denotes the second eigenv alue of the Dirichlet Laplacian on $A$.\n\nIn this talk we show that any o ptimal set $\\Omega$ for \\eqref{eq:main} is equivalent to the union of tw o disjoint open sets\, $\\Omega^\\pm$\, which are $C^{1\,\\alpha}$ regular up to a (possibly empty) closed singular set of Hausdorff dimension at mo st $d-5$\, which is contained in the one-phase free boundaries.\n\nIn part icular\, we are able to prove that the set of two-phase points\, that is\, $\\partial \\Omega^+\\cap \\partial \\Omega^-\\cap D$\, is contained in t he regular set.\n\n\nThis is a joint work with Baptiste Trey and Bozhidar Velichkov.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriele Benomio (Princeton University) DTSTART:20210318T140000Z DTEND:20210318T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/32 DESCRIPTION:Title: A new instability for higher dimensional black holes\nby Ga briele Benomio (Princeton University) as part of Lisbon webinar in analysi s and differential equations\n\n\nAbstract\nThe dynamics of solutions to t he Einstein equations is richer in dimensions higher than $3+1$. In contra st with the classical stability of stationary\, asymptotically flat black hole solutions in $3+1$ dimensions\, some families of higher dimensional b lack holes suffer from dynamical instabilities. I will discuss a subtle in stability affecting a wide class of higher dimensional black holes which h as not been previously observed in the literature. This new instability is \, in a sense\, more fundamental than the other known instability phenomen a in higher dimensions and can be related to a precise geometric property of the class of spacetimes considered.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Shrish Parmeshwar (University of Bath) DTSTART:20210318T150000Z DTEND:20210318T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/33 DESCRIPTION:Title: Global-in-Time Solutions to the N-Body Euler-Poisson System \nby Shrish Parmeshwar (University of Bath) as part of Lisbon webinar in a nalysis and differential equations\n\n\nAbstract\nWe investigate the $N$-B ody compressible Euler-Poisson system\, modelling multiple stars interacti ng with each other via Newtonian gravity. If we prescribe initial data so that each star expands indefinitely\, one might expect that two of them wi ll collide in finite time due to their expansion\, and the influence of gr avity. In this talk we show that there exists a large family of initial po sitions and velocities for the system such that each star can expand for a ll time\, but no two will touch in finite time. To do this we use scaling mechanisms present in the compressible Euler system\, and a careful analys is of how the gravitational interaction between stars affects their dynami cs.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Harbir Antil (George Mason University) DTSTART:20210211T140000Z DTEND:20210211T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/34 DESCRIPTION:Title: Fractional PDEs: Control\, Numerics\, and Applications\nby Harbir Antil (George Mason University) as part of Lisbon webinar in analys is and differential equations\n\n\nAbstract\nFractional calculus and its a pplication to anomalous diffusion has recently received a tremendous amoun t of attention. In complex/heterogeneous material mediums\, the long-range correlations or hereditary material properties are presumed to be the cau se of such anomalous behavior. Owing to the revival of fractional calculus \, these effects are now conveniently modeled by fractional-order differen tial operators and the governing equations are reformulated accordingly. S imilarly\, the potential of fractional operators has been harnessed in var ious scientific domains like geophysical electromagnetics\, imaging scienc e\, deep learning\, etc. \n\nIn this talk\, fractional operators will be introduced and both linear and nonlinear\, fractional-order differential e quations will be discussed. New notions of optimal control and optimizatio n under uncertainty will be presented. Several applications from geophysic s\, imaging science\, and deep learning will be presented.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Paolo Gidoni (Czech Academy of Sciences) DTSTART:20210218T140000Z DTEND:20210218T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/35 DESCRIPTION:Title: A vanishing inertia analysis for finite dimensional rate-indepe ndent systems and an application to soft crawlers\nby Paolo Gidoni (Cz ech Academy of Sciences) as part of Lisbon webinar in analysis and differe ntial equations\n\n\nAbstract\nThe quasistatic limit is a convenient appro ximation in the modelling of several (suitable) mechanical systems\, when the evolution occurs at a sufficiently slow time-scale. In this talk we di scuss the validity of the quasistatic approximation in finite-dimensional rate-independent systems via a vanishing-inertia asymptotic analysis of dy namic evolutions. More precisely\, we show the uniform convergence of dyna mic solutions to the quasistatic one\, employing the concept of energetic solution. Our work is motivated by the application to a family of models f or biological and bio-inspired crawling locomotion. Hence a part of the se minar will focus on modelling: we will discuss how soft crawlers can be ef fectively described in our theoretical framework and briefly survey the re levance\, or lack thereof\, of inertia in some locomotion strategies. By a technical point of view\, our application requires time-dependence of the dissipation potential and translation invariance of the potential energy. \n\nJoint work with Filippo Riva (http://arxiv.org/abs/2007.09069 ).\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Premoselli (Université Libre de Bruxelles) DTSTART:20210311T140000Z DTEND:20210311T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/36 DESCRIPTION:Title: Towers of bubbles for Yamabe-type equations in dimensions large r than 7\nby Bruno Premoselli (Université Libre de Bruxelles) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nI n this talk we consider perturbations of Yamabe-type equations on closed R iemannian manifolds. In dimensions larger than 7 and on locally conformall y flat manifolds we construct blowing-up solutions that behave like towers of bubbles concentrating at a critical point of the mass function. Our re sult does not assume any symmetry on the underlying manifold.\n\nWe perfor m our construction by combining finite-dimensional reduction methods with a linear blow-up analysis in order to sharply control the remainder of the construction in strong spaces. Our approach works both in the positive an d sign-changing case. As an application we prove the existence\, on a gene ric bounded open set of $\\mathbb{R}^n$\, of blowing-up solutions of the B rézis-Nirenberg equation that behave like towers of bubbles of alternatin g signs.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Valeria Chiadò Piat (Politecnico di Torino) DTSTART:20210408T130000Z DTEND:20210408T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/37 DESCRIPTION:Title: An extension theorem from connected sets and homogenization of non-local functionals\nby Valeria Chiadò Piat (Politecnico di Torino) as part of Lisbon webinar in analysis and differential equations\n\n\nAbs tract\nExtensions operators are a classical tool to provide uniform estima tes and gain compactness in the homogenization of integral functionals ove r perforated domains. In this talk we discuss the case of non-local functi onals. The results are obtained in collaboration with Andrea Braides and L orenza D'Elia.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicola Fusco (Università di Napoli "Federico II") DTSTART:20210415T130000Z DTEND:20210415T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/38 DESCRIPTION:Title: Asymptotic stability for the gradient flow of some nonlocal ene rgies\nby Nicola Fusco (Università di Napoli "Federico II") as part o f Lisbon webinar in analysis and differential equations\n\n\nAbstract\nI w ill start by discussing some recent results on the asymptotic stability of the $H^{-1}$-gradient flow of the perimeter\, the so called surface diffu sion. Then I will consider the $H^{-1}$-gradient flow of some energy funct ionals given by the area of an interface plus a non local volume term. Thi s is a joint work with E. Acerbi\, V. Julin and M. Morini\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Grégoire Allaire (CMAP\, Ecole Polytechnique) DTSTART:20210401T130000Z DTEND:20210401T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/39 DESCRIPTION:Title: Some problems and some solutions in shape and topology optimiza tion of structures built by additive manufacturing\nby Grégoire Allai re (CMAP\, Ecole Polytechnique) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nAdditive manufacturing (or 3-d print ing) is a new exciting way of building structures without any restriction on their topologies. However\, it comes with its own difficulties or new i ssues. Therefore\, it is a source of many interesting new problems for opt imization. I shall discuss two of them and propose solutions to these prob lems\, but there is still a lot of room for improvement!\n\nFirst\, additi ve manufacturing technologies are able to build finely graded microstructu res (called lattice materials). Their optimization is therefore an importa nt issue but also an opportunity for the resurrection of the homogenizatio n method ! Indeed\, homogenization is the right technique to deal with mic rostructured materials where anisotropy plays a key role\, a feature which is absent from more popular methods\, like SIMP. I will describe recent w ork on the topology optimization of these lattice materials\, based on a c ombination of homogenization theory and geometrical methods for the overal l deformation of the lattice grid.\n\nSecond\, additive manufacturing\, es pecially in its powder bed fusion technique\, is a very slow process becau se a laser beam must travel along a trajectory\, which covers the entire s tructure\, to melt the powder. Therefore\, the optimization of the laser p ath is an important issue. Not only do we propose an optimization strategy for the laser path\, but we couple it with the usual shape and topology o ptimization of the structure. Numerical results show that these two optimi zations are tightly coupled.\n\nThis is a joint work with many colleagues\ , including two former PhD students\, P. Geoffroy-Donders and M. Boissier. \n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Riccardo Scala (Università degli Studi di Siena) DTSTART:20210415T140000Z DTEND:20210415T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/40 DESCRIPTION:Title: Nonlocality features of the area functional and the Plateau pro blem\nby Riccardo Scala (Università degli Studi di Siena) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe br iefly discuss the definition of relaxation of the area functional. The rel axed area functional\, denoted by $A$\, extends the classical area functio nal\, which\, for any "regular" map $v:U\\subset \\mathbb{R}^n\\rightarrow \\mathbb{R}^N$ evaluates the $n$-dimensional area of its graph over $U$. The problem of determining the domain and the expression of $A$ is open in codimension greater than 1. Specifically\, this relaxed functional turns out to be nonlocal and cannot be expressed by an integral formula. We disc uss how it is related to classical and nonclassical versions of the Platea u problem. As a main example\, we try to understand what is the relaxed gr aph of the function $x/|x|$\, a question that surprisingly remained open f or decades.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Yukihiko Nakata (Aoyama Gakuin University) DTSTART:20210325T140000Z DTEND:20210325T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/41 DESCRIPTION:Title: Period two solution for a class of distributed delay differenti al equations\nby Yukihiko Nakata (Aoyama Gakuin University) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe c onsider a periodic solution for a class of distributed delay differential equations.\n\nA period two solution for distributed delay differential equ ations\, where the period is twice the maximum delay\, is shown to satisfy a Hamiltonian system of ordinary differential equations\, from which we c an construct the period two solution for the distributed delay differentia l equation.\n\nThe idea is based on Kaplan & Yorke (1974\, JMAA) for a dis crete delay differential equation. We present distributed delay differenti al equations that have periodic solutions expressed in terms of the Jacobi elliptic functions.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Juan Luis Vásquez (Universidad Autónoma de Madrid) DTSTART:20210422T130000Z DTEND:20210422T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/42 DESCRIPTION:Title: The theory of fractional p-Laplacian equations\nby Juan Lui s Vásquez (Universidad Autónoma de Madrid) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe consider the time-de pendent fractional p-Laplacian equation with parameter $p>1$ and fractiona l exponent $0Homogenisation of discrete dynamical optimal transport\nby Jan Mass (IST Austria) as part of Lisbon webinar in analysis and different ial equations\n\n\nAbstract\nMany stochastic systems can be viewed as grad ient flow ('steepest descent') in the space of probability measures\, wher e the driving functional is a relative entropy and the relevant geometry i s described by a dynamical optimal transport problem. In this talk we focu s on these optimal transport problems and describe recent work on the limi t passage from discrete to continuous.\nSurprisingly\, it turns out that d iscrete transport metrics may fail to converge to the expected limit\, eve n when the associated gradient flows converge. We will illustrate this phe nomenon in examples and present a recent homogenisation result.\n\nThis ta lk is based on joint work with Peter Gladbach\, Eva Kopfer\, and Lorenzo P ortinale.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Max Fathi (Université de Paris) DTSTART:20210429T140000Z DTEND:20210429T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/44 DESCRIPTION:Title: A proof of the Caffarelli contraction theorem via entropic inte rpolation\nby Max Fathi (Université de Paris) as part of Lisbon webin ar in analysis and differential equations\n\n\nAbstract\nThe Caffarelli co ntraction theorem states that optimal transport maps (for the quadratic co st) from a Gaussian measure onto measures that satisfy certain convexity p roperties are globally Lipschitz\, with a dimension-free estimate. It has found many applications in probability\, such as concentration and functio nal inequalities. In this talk\, I will present an alternative proof\, usi ng entropic interpolation and variational arguments. Joint work with Natha el Gozlan and Maxime Prod'homme.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone DiMarino (Università di Genova) DTSTART:20210513T130000Z DTEND:20210513T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/45 DESCRIPTION:by Simone DiMarino (Università di Genova) as part of Lisbon w ebinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Didier Pilod (University of Bergen) DTSTART:20210506T130000Z DTEND:20210506T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/46 DESCRIPTION:Title: Global well-posedness and scattering for the Dysthe equation in $L^2(\\mathbb{R}^2)$\nby Didier Pilod (University of Bergen) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nTh e Dysthe equation is a higher order approximation of the water waves syste m in the modulation (Schrödinger) regime and in the infinite depth case. After reviewing the derivation of the Dysthe and related equations\, we wi ll focus on the initial-value problem. We prove a small data global well-p osedness and scattering result in the critical space $L^2(\\mathbb R^2)$. This result is sharp in view of the fact that the flow map cannot be $C^3$ continuous below $L^2(\\mathbb R^2)$.\n\nOur analysis relies on linear an d bilinear Strichartz estimates in the context of the Fourier restriction norm method. Moreover\, since we are at a critical level\, we need to work in the framework of the atomic space $U^2_S $ and its dual $V^2_S $ of sq uare bounded variation functions.\n\nWe also prove that the initial-value problem is locally well-posed in $H^s(\\mathbb R^2)$\, $s\\gt 0$.\n\nOur r esults extend to the finite depth version of the Dysthe equation.\nThis ta lk is based on a joint work with Razvan Mosincat (University of Bergen) an d Jean-Claude Saut (Université Paris-Saclay).\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Mariana Smit Vega Garcia (Western Washington University) DTSTART:20210520T130000Z DTEND:20210520T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/47 DESCRIPTION:Title: Regularity of almost minimizers with free boundary\nby Mari ana Smit Vega Garcia (Western Washington University) as part of Lisbon web inar in analysis and differential equations\n\n\nAbstract\nWe study almost minimizer for functionals that yield a free boundary\, as in the work of Alt-Caffarelli and Alt-Caffarelli-Friedman. The almost minimizing property can be understood as the defining characteristic of a minimizer in a prob lem that explicitly takes noise into account. In this talk\, we discuss th e regularity of almost minimizers to energy functionals with variable coef ficients. This is joint work with Guy David\, Max Engelstein & Tatiana Tor o.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Julio D. Rossi (Universidad de Buenos Aires) DTSTART:20210527T130000Z DTEND:20210527T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/48 DESCRIPTION:Title: Non Linear Mean Value Properties for Monge-Ampère Equations\nby Julio D. Rossi (Universidad de Buenos Aires) as part of Lisbon webin ar in analysis and differential equations\n\n\nAbstract\nIn recent years t here has been an increasing interest in whether a mean value property\, kn own to characterize harmonic functions\, can be extended in some weak form to solutions of nonlinear equations. This question has been partially mot ivated by the surprising connection between Random Tug-of-War games and t he normalized $p-$Laplacian discovered some years ago\, where a nonlinear asymptotic mean value property for solutions of a PDE is related to a dyna mic programming principle for an appropriate game.\nOur goal in this talk is to show that an asymptotic nonlinear mean value formula holds for the classical Monge-Ampère equation.\nJoint work with P. Blanc (Jyvaskyla)\, F. Charro (Detroit)\, and J.J. Manfredi (Pittsburgh).\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafael Benguria (PUC Chile) DTSTART:20210930T130000Z DTEND:20210930T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/49 DESCRIPTION:Title: Gagliardo-Nirenberg-Sobolev Inequalities and their counterparts on bounded domains\nby Rafael Benguria (PUC Chile) as part of Lisbon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Monica Clapp (Universidad Nacional Autónoma de México) DTSTART:20211007T130000Z DTEND:20211007T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/50 DESCRIPTION:Title: Optimal partitions for the Yamabe equation\nby Monica Clapp (Universidad Nacional Autónoma de México) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nThe Yamabe equation on a Riemannian manifold $(M\,g)$ is relevant to the question of finding a co nstant scalar curvature metric on $M$ that is conformally equivalent to th e given one.\n\nAn optimal $\\ell$-partition for the Yamabe equation is a cover of $M$ by $\\ell$ pairwise disjoint open subsets such that the Yamab e equation with Dirichlet boundary condition has a least energy solution o n each one of these sets\, and the sum of the energies of these solutions is minimal.\n\nWe will present some recent results obtained in collaborati on with Angela Pistoia (La Sapienza Università di Roma) and Hugo Tavares (Universidade de Lisboa) that establish the existence and qualitative prop erties of such partitions.\n\nIf time allows\, we will also present some r esults on symmetric optimal partitions obtained in collaboration with Ange la Pistoia\, and with Alberto Saldaña (UNAM) and Andrzej Szulkin (Stockho lm University).\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Juraj Földes (University of Virginia) DTSTART:20211014T150000Z DTEND:20211014T160000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/51 DESCRIPTION:Title: Stochastic approach to boundary regularity of hypoelliptic PDEs \nby Juraj Földes (University of Virginia) as part of Lisbon webinar in analysis and differential equations\n\n\nAbstract\nWe will discuss the almost sure behavior of solutions of stochastic differential equations(SDE s) as time goes to zero. Our main general result establishes a functional law of the iterated logarithm (LIL) that applies in the setting of SDEs wi th degenerate noise satisfying the weak Hormander condition. We will intro duce large deviations to provide some details of proofs. Furthermore\, we apply the stochastic results to the problem of identifying regular points for hypoelliptic diffusions and obtain criteria for well posedness of dege nerate equations.\n\nThis is a joint work with David Herzog and Marco Carf agnini\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone Dovetta (Università degli Studi di Roma "La Sapienza") DTSTART:20211021T130000Z DTEND:20211021T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/52 DESCRIPTION:Title: Action versus energy ground states in nonlinear Schrödinger eq uations\nby Simone Dovetta (Università degli Studi di Roma "La Sapien za") as part of Lisbon webinar in analysis and differential equations\n\n\ nAbstract\nThe talk investigates the relations between normalized critical points of the nonlinear Schrödinger energy functional and critical point s of the corresponding action functional on the associated Nehari manifold .\n\nFirst\, we show that the ground state levels are strongly related by the following duality result: the (negative) energy ground state level is the Legendre—Fenchel transform of the action ground state level. Further more\, whenever an energy ground state exists at a certain frequency\, the n all action ground states with that frequency have the same mass and are energy ground states too. We see that the converse is in general false and that the action ground state level may fail to be convex. Next we analyze the differentiability of the ground state action level and we provide an explicit expression involving the mass of action ground states. Finally we show that similar results hold also for local minimizers\, and we exhibit examples of domains where our results apply.\n\nThe matter of the talk re fers to joint works with Enrico Serra and Paolo Tilli.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Kelei Wang (Wuhan University) DTSTART:20211104T140000Z DTEND:20211104T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/53 DESCRIPTION:Title: Regularity of transition layers in Allen-Cahn equation\nby Kelei Wang (Wuhan University) as part of Lisbon webinar in analysis and di fferential equations\n\n\nAbstract\nIn this talk I will survey the regular ity theory for transition layers in singularly perturbed Allen-Cahn equati on\, from zeroth order regularity to second order one. Some applications o f this regularity theory will also be discussed\, including De Giorgi conj ecture\, classification of finite Morse index solutions and construction o f minimal hypersurfaces by Allen-Cahn approximation.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Bellettini (ICTP and Università di Siena) DTSTART:20211118T140000Z DTEND:20211118T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/54 DESCRIPTION:Title: On a conjecture of De Giorgi on the first variation of the Modi ca-Mortola functional\nby Giovanni Bellettini (ICTP and Università di Siena) as part of Lisbon webinar in analysis and differential equations\n \n\nAbstract\nWe shall discuss some (not so recent) results on a 1991 conj ecture of De Giorgi concerning the Gamma limit of the square norm of the f irst variation of the Modica-Mortola functionals\, and its relation with t he Willmore functional.\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Van Schaftingen (Université Catholique de Louvain) DTSTART:20211202T140000Z DTEND:20211202T150000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/55 DESCRIPTION:Title: Ginzburg-Landau functionals on planar domains for a general com pact vacuum manifold\nby Jean Van Schaftingen (Université Catholique de Louvain) as part of Lisbon webinar in analysis and differential equatio ns\n\n\nAbstract\n**PostPoned**\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/55/ END:VEVENT BEGIN:VEVENT SUMMARY:João Pedro Ramos (ETH Zurich) DTSTART:20220615T130000Z DTEND:20220615T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/56 DESCRIPTION:Title: Time-frequency localisation operators\, their eigenvalues and r elationship to elliptic PDE\nby João Pedro Ramos (ETH Zurich) as part of Lisbon webinar in analysis and differential equations\n\nAbstract: TBA \n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergei Kuksin (Univ. Paris VII) DTSTART:20220617T100000Z DTEND:20220617T110000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/57 DESCRIPTION:Title: Kolmogorov theory of turbulence and a rigorous theory of one-di mensional turbulence\nby Sergei Kuksin (Univ. Paris VII) as part of Li sbon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Marroquin (Universidade Federal do Rio de Janeiro) DTSTART:20220628T130000Z DTEND:20220628T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/58 DESCRIPTION:Title: Stochastic two-scale Young measures and homogenization of conse rvation laws with multiplicative noise\nby Daniel Marroquin (Universid ade Federal do Rio de Janeiro) as part of Lisbon webinar in analysis and d ifferential equations\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Hermano Frid (Instituto de Matemática Pura e Aplicada) DTSTART:20220629T130000Z DTEND:20220629T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/59 DESCRIPTION:Title: On short wave-long wave interactions in the relativist context< /a>\nby Hermano Frid (Instituto de Matemática Pura e Aplicada) as part of Lisbon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Jörg Wolf (Chung-Ang University) DTSTART:20220721T130000Z DTEND:20220721T140000Z DTSTAMP:20260404T111008Z UID:LisbonWADE/60 DESCRIPTION:Title: Existence of weak solutions the equations of a non-Newtonian fl uid with non standard growth\nby Jörg Wolf (Chung-Ang University) as part of Lisbon webinar in analysis and differential equations\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/LisbonWADE/60/ END:VEVENT END:VCALENDAR