BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tere M-Seara (UPC\, Barcelona) DTSTART:20200630T123000Z DTEND:20200630T133000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/1 DESCRIPTION:Title: Mechanism of instability in Hamiltonian Systems: Sk ipping along a normally hyperbolic invariant manifold\nby Tere M-Seara (UPC\, Barcelona) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\ nLecture held in Via Microsoft Teams.\n\nAbstract\nWe describe a recent me thod to show instability in Hamiltonian systems. The mechanism works if so me explicit and verifiable transversality conditions are satisfied. The hy pothesis can be verified by just checking that some Melnikov type integral s have non-degenerate zeros. This holds for Baire generic sets of perturba tions in the C^r topology.\n\nThe method uses these hypotheses to conclude the existence of orbits\, in near integrable Hamiltonian Systems\, which change the action coordinate by a quantity independent of the size of the perturbation.\n\nnstructions: the Seminar will be held in streaming\, as a videoconference on-line\, via Microsoft Teams.\nLink: https://teams.micro soft.com/l/meetup-join/19%3a851c456a7d9d47caae6f7d5534a315f3%40thread.tacv 2/1592845825482?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae4 7d0e%22%2c%22Oid%22%3a%229bfb10cf-6b03-47dc-906c-d23eb368824c%22%7d\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Giuseppe Devillanova (Politecnico di Bari) DTSTART:20201029T130000Z DTEND:20201029T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/2 DESCRIPTION:Title: Profile decomposition and applications\nby Gius eppe Devillanova (Politecnico di Bari) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nAbs tract. A brief survey on the evolution of concentration - com-\npactness t heorems in the last 30 years is given. Starting from the\npioneering resul ts by P-L Lions in [5] and M. Struwe in [8] for\nP.S. sequences and relati ve generalizations to bounded sequences\nin [6]\, with their “wavelet ba sed” counterpart in [3] and [4] (see\n[2] for a comparison between the t wo approaches in Lp spaces)\,\nthe research path has evolved till [7] wher e the results are given\nin a more general context (uniformly convex Banac h spaces). In\nthe spirit of the “compactness and contradiction” argum ent by T.\nTao [9]\, some applications are provided in [1] to prove existe nce of\ninfinitely many solutions to some elliptic equations.\nReferences\ n[1] G. Devillanova\, S. Solimini\, Infinitely many positive solutions to some non-\nsymmetric scalar field equations: the planar case. Calculus of Variations and\nPartial Differential Equations 52 (2015)\, Issue 3-4\, 857 -898.\n[2] G. Devillanova\, S. Solimini\, Some Remarks on Profile Decompos ition Theo-\nrems. preprint.\n[3] P. G ́erard\, Description du d ́efaut de compacit ́e de l’injection de Sobolev.\nESAIM: Control\, Optimisatio n and Calculus of Variations 3 (1998)\, 213-233.\n[4] S. Jaffard\, Analysi s of the lack of compactness in the critical Sobolev embed-\ndings J. Func t. Anal.\, 161 (1999)\, pp. 384–396.\n[5] P-L. Lions\, The concentration -compactness principle in the calculus of vari-\nations. The locally compa ct case. Parts 1 and 2\, Annales de l’IHP\, Analyse\nnon-lin ́eaire\, I (1984)\, 109-145 and 224-283.\n[6] S. Solimini\, A note on Compactness-ty pe properties with respect to Lorentz\nnorms of bounded subsets of a Sobol ev space. Ann. Inst. Henry Poincar ́e 12\, 3\n(1995)\, 319–337.\n[7] S. Solimini\, K. Tintarev\, Concentration analysis in Banach spaces.\nCommun ications\n in\n Contemporary\n Mathematics\n (2015)\,\n DOI:\n10.1142/S021 9199715500388.\n[8] M. Struwe\, A global compactness result for elliptic b oundary value problems\ninvolving limiting nonlinearities. Math. Z. 187 (1 984)\, pp. 511-517.\n[9] T. Tao\, Compactness and contradiction.\nhttps:// terrytao.files.wordpress.com/2011/06/blog-book.pdf\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 2/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudianor Alves (Universidade Federal de Campina Grande) DTSTART:20201112T130000Z DTEND:20201112T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/3 DESCRIPTION:Title: Super-critical Neumann problems on unbounded domain s\nby Claudianor Alves (Universidade Federal de Campina Grande) as par t of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Micr osoft Teams.\n\nAbstract\nIn this paper\, by making use of  a new variati onal principle\,  we prove  existence of nontrivial solutions for two di fferent  types of semilinear problems with Neumann boundary conditions in   unbounded  domains. Namely\, we study elliptic equations and Hamiltoni an systems  on the unbounded domain  $\\Omega=\\R^{​​​m}​​​\ \times B_r$ where   $B_r$ is a ball  centered at the origin with radius   $r$ in $\\mathbb{​​​R}​​​^{​​​n}​​​$.  Our pro ofs consist of several new and novel ideas that can be used in broader con texts. This is a joint work with Abbas Moameni that was accepted for publi cation in Nonlinearity.\n\n N.B.: this talk is part of the activity of the Italian MIUR Excellence Department Project CUP E83C18000100006\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 3/ END:VEVENT BEGIN:VEVENT SUMMARY:Sara Daneri (Gran Sasso Science Institute) DTSTART:20201119T130000Z DTEND:20201119T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/4 DESCRIPTION:Title: Symmetry breaking for local/nonlocal interaction fu nctionals\nby Sara Daneri (Gran Sasso Science Institute) as part of An alysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft T eams.\n\nAbstract\nIn this talk I will review some recent results obtained in collaboration with E. Runa and A. Kerschbaum on the one-dimensionality of the minimizers of a family of continuous local/nonlocal interaction fu nctionals in general dimension. Such functionals have a local term\, typic ally the perimeter or its Modica-Mortola approximation\, which penalizes i nterfaces\, and a nonlocal term favouring oscillations which are high in f requency and in amplitude. The competition between the two terms is expect ed by experiments and simulations to give rise to periodic patterns at equ ilibrium. Functionals of this type are used to model pattern formation\, e ither in material science or in biology. The difficulty in proving the eme rgence of such structures is due to the fact that the functionals are symm etric with respect to permutation of coordinates\, while minimizers are no t. We will present new techniques and results showing that for two classes of functionals (used to model generalized anti-ferromagnetic systems\, re spectively colloidal suspensions)\, both in sharp interface and in diffuse interface models\, minimizers are one-dimensional and periodic\, in gener al dimension. In the discrete setting such results had been previously obt ained for a smaller set of functionals with a different approach by Giulia ni and Seiringer. \n N.B.: this talk is part of the activity of the MIU R Excellence Department Project CUP E83C18000100006 \n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 4/ END:VEVENT BEGIN:VEVENT SUMMARY:Elsa Marchini (Politecnico di Milano) DTSTART:20201126T130000Z DTEND:20201126T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/5 DESCRIPTION:Title: Minimal time optimal control for the moon lander p roblem\nby Elsa Marchini (Politecnico di Milano) as part of Analysis S eminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\ nAbstract\nWe study a variant of the classical safe landing optimal contro l problem in aerospace\, introduced by Miele in the Sixties\, where the ta rget was to land a spacecraft on the moon by minimizing the consumption of fuel. Assuming that the spacecraft has a failure and that the thrust (rep resenting the control) can act in both vertical directions\, the new targe t becomes to land safely by minimizing time\, no matter of what the consum ption is. In dependence of the initial data (height\, velocity\, and fuel) \, we prove that the optimal control can be of four different kinds\, all being piecewise constant. Our analysis covers all possible situations\, in cluding the nonexistence of a safe landing strategy due to the lack of fue l or for heights/velocities for which also a total braking is insufficient to stop the spacecraft.\n
\nTalk based on a joint work with Filippo Ga zzola\n
\n N.B.: this talk is part of the activity of the MIUR Excel lence Department Project CUP E83C18000100006 \n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 5/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriele Benedetti (Heidelberg University) DTSTART:20201210T130000Z DTEND:20201210T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/6 DESCRIPTION:Title: Strong magnetic fields on surfaces: trapped motions and fully periodic systems\nby Gabriele Benedetti (Heidelberg Univers ity) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nIt is a central problem in experiment al physics to design magnetic fields that trap charged particles in a regi on of space. In this talk\, we show how to use the KAM theorem to trap par ticles constrained on a surface if the magnetic field is strong and certai n non-degenerate conditions on the field or on the curvature of the surfac e are satisfied. Using similar ideas we show that the motion of a particle in a strong magnetic field is periodic for every initial condition if and only if the field is constant and the surface has constant curvature. Thi s is joint work with Luca Asselle.\n\nMS Teams Link for the streaming: \nh ttps://teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1145dfae91372d186b 1cd9%40thread.tacv2/1606733297311?context=%7b%22Tid%22%3a%2224c5be2a-d764- 40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c35-88e4-99bf4cf 68fe9%22%7d\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 6/ END:VEVENT BEGIN:VEVENT SUMMARY:Vitaly Moroz (Swansea University) DTSTART:20201210T130000Z DTEND:20201210T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/7 DESCRIPTION:Title: Asymptotic profiles of groundstates for a class of Choquard equations\nby Vitaly Moroz (Swansea University) as part of An alysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft T eams.\n\nAbstract\nWe study the asymptotic behaviour of groundstates for a class of singularly perturbed Choquard type equations with a local repuls ion term. We identify seven different asymptotic regimes and provide a cha racterisation of the limit profiles of the groundstates when perturbation parameter is small. We also outline the behaviour of groundstates when per turbation is strong. This is a joint work with Zeng Liu (Suzhou\, China).\ n\n NB : this talk is part of the activity of the MIUR Excellenc e Department Project CUP E83C18000100006\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 7/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Muratori (Politecnico di Milano) DTSTART:20210114T130000Z DTEND:20210114T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/8 DESCRIPTION:Title: Nonlinear diffusion equations on noncompact manifol ds and relations with stochastic completeness\nby Matteo Muratori (Pol itecnico di Milano) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n \nLecture held in Via Microsoft Teams.\n\nAbstract\nWe prove that the mass conservation property for the heat flow on a complete\, connected\, nonco mpact Riemannian manifold $M$\, namely stochastic completeness\, is equiva lent to the uniqueness of nonnegative bounded solutions for a certain clas s of nonlinear evolution equations. Such a connection was well known in th e pure linear case only\, i.e. for the heat equation itself. Here we consi der equations of the type of $u_t=\\Delta(\\phi(u))$\, where $\\phi$ is an y nonnegative\, concave\, increasing function\, $C^1$ away from the origin and satisfying $ \\phi(0)=0 $. We provide optimal criteria for uniqueness /nonuniqueness of nonnegative\, bounded (distributional) solutions taking general nonnegative\, bounded initial data $u_0$. In particular our result s apply to the fast diffusion equation $u_t=\\Delta(u^m)$ (where $m \\in ( 0\,1)$)\, and they show that there is a large class of manifolds in which uniqueness actually fails. This is in sharp contrast\, for instance\, with the Euclidean case\, where existence and uniqueness hold for merely $L^1_ {loc}$ initial data thanks to the theory developed by M.A. Herrero and M. Pierre in the '80s. We will also address existence/nonexistence of nonnega tive\, nontrivial\, bounded solutions to a strictly related nonlinear elli ptic equation and\, if time allows\, some work in progress devoted to remo ving the concavity assumption. \n\n\nThe talk is based on joint projects w ith G. Grillo\, K. Ishige and F. Punzo.\n\nNote: This talk is pa rt of the activity of the MIUR Excellence Department Project CUP E83C18000 100006\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 8/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessandra Pluda (University of Pisa) DTSTART:20210121T130000Z DTEND:20210121T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/9 DESCRIPTION:Title: Motion by curvature of networks: analysis of singul arities and “restarting” theorems\nby Alessandra Pluda (University of Pisa) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nA regular network is a finite un ion of sufficiently smooth\ncurves whose end points meet in\ntriple juncti ons. I will present the state-of-the-art of the problem of\nthe motion by curvature of a regular network\nin the plane mainly focusing on singularit y formation. Then I will\ndiscuss the need of a “restarting”\ntheorem for networks with multiple junctions of order bigger than three\nand I wil l give an idea of a possible strategy to prove it.\nThis is a research in collaboration with Jorge Lira (University of\nFortaleza)\, Rafe Mazzeo (St anford University) and Mariel Saez (P.\nUniversidad Catolica de Chile).\n \nNote: This talk is part of the activity of the MIUR Excellence Departmen t Project MATH@TOV CUP E83C18000100006\n\nThe talk will be streamed via MS Teams:\nhttps://teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1145dfae 91372d186b1cd9%40thread.tacv2/1610381100098?context=%7b%22Tid%22%3a%2224c5 be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c35-88 e4-99bf4cf68fe9%22%7d\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 9/ END:VEVENT BEGIN:VEVENT SUMMARY:Lorenzo Valvo (University of Rome Tor Vergata) DTSTART:20210204T130000Z DTEND:20210204T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/10 DESCRIPTION:Title: Hamiltonian Control of Magnetic Field Lines: Compu ter Assisted Results Proving the Existence of KAM Barriers\nby Lorenzo Valvo (University of Rome Tor Vergata) as part of Analysis Seminar @ Univ . Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nA control theory for Hamiltonian systems\, based on KAM theory\, was introdu ced in [Ciraolo\, 2004] and applied to a model of magnetic field in [Chand re\, 2006]. By a combination of Frequency Analysis and of a rigorous (Comp uter Assisted) KAM algorithm we show that in the phase space of the magnet ic field\, due to the control term\, a set of invariant tori appears\, and it acts as a transport barrier. Our analysis\, which is common (but often also limited) to celestial mechanics\, is very general and can be applied to quasi-integrable Hamiltonian systems satisfying a few additional mild assumptions.\n\nNote: This talk is part of the activity of the MIUR Excell ence Department Project MATH@TOV CUP E83C18000100006\n\nThe talk will be s treamed via MS Teams:\nhttps://teams.microsoft.com/l/meetup-join/19%3a7f27 3a2aff1145dfae91372d186b1cd9%40thread.tacv2/1611256564820?context=%7b%22Ti d%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fe a-2e4d-4c35-88e4-99bf4cf68fe9%22%7d\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 10/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Martinazzi (Universita' di Padova) DTSTART:20210211T130000Z DTEND:20210211T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/11 DESCRIPTION:Title: Entire solutions to a prescribed curvature equatio n in R^4 and the Nirenberg problem\nby Luca Martinazzi (Universita' di Padova) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture h eld in Via Microsoft Teams.\n\nAbstract\nSeveral existence and non-existen ce results for the Nirenberg problem of prescribing the Gauss curvature on a closed surface are classically known. In higher dimension\, analog resu lts hold with the Q-curvature replacing the Gauss curvature. In many cases a non-existence result is associated with a blow-up phenomenon which lead s to entire solutions of the Liouville equation $-\\Delta u = e^{​​​ 2u}​​​$ in dimension 2 or higher-dimensional analogs. On the other h and\, Borer\, Galimberti and Struwe studied a blow-up phenomenon which cou ld lead to solutions to the equation\n$$-\\Delta u =(1-|x|^2)e^{​​​2 u}​​​ in R^2$$ (1)\nor\n$$\\Delta^2 u =(1-|x|^2)e^{​​​4u}​ ​​ in R^4$$ (2)\nWhile non-existence results have been shown for (1) b y Struwe\, the question remained opened for (2). We recently gave a positi ve answer with A. Hyder\, giving sharp conditions under which (2) admits s olutions with controlled behaviour at infinity\, hence answering an open q uestion by Struwe. More related open questions will be discussed.\n\nN. B. This talk is part of the activity of the MIUR Excellence Departm ent Project CUP E83C18000100006.\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 11/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacopo Bellazzini (Università di Pisa) DTSTART:20210225T130000Z DTEND:20210225T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/12 DESCRIPTION:Title: Ground state energy threshold and blow-up for NLS with competing nonlinearities\nby Jacopo Bellazzini (Università di Pi sa) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held i n Via Microsoft Teams.\n\nAbstract\nAim of the talk is to discuss qualitat ive properties of the nonlinear Schr\\"odinger equation with combined nonl inearities\, where the leading term is an intracritical focusing power-typ e nonlinearity\, and the perturbation is given by a power-type defocusing one. Fixed the mass of the problem\, we completely answer the question we ther the ground state energy \, which is a threshold between global existe nce and formation of singularities\, is achieved. As a byproduct of the va riational characterization of the ground state energy\, we show the existe nce of blowing-up solutions in finite time\, for any initial data with ene rgy below the ground state energy threshold in case of cylindrical symmetr y.\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 12/ END:VEVENT BEGIN:VEVENT SUMMARY:Weiwei Ao (Wuhan University) DTSTART:20210304T130000Z DTEND:20210304T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/13 DESCRIPTION:Title: Symmetry and symmetry breaking for the fractional Caffarelli-Kohn-Nirenberg inequality\nby Weiwei Ao (Wuhan University) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Vi a Microsoft Teams.\n\nAbstract\nWe first study the existence and nonexiste nce of extremal solutions. We also show some results for the symmetry and symmetry breaking region for the minimizers. In order to get these result we reformulate the fractional Caffarelli-Kohn-Nirenberg inequality in cyli ndrical variables. We also get the non-degeneracy and uniqueness of minimi zers in the radial symmetry class. This is joint work with Azahara DelaTor re and Maria del Mar Gonzalez.\n
\nN.B.:  \;this talk is part of the activity of the MIUR Excellence Department Project CUP E83C180 00100006\n\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 13/ END:VEVENT BEGIN:VEVENT SUMMARY:Mohameden Ahmedou (Universität Gießen) DTSTART:20210311T130000Z DTEND:20210311T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/14 DESCRIPTION:Title: New blow up phenomena for the Nirenberg's pr oblem on half spheres\nby Mohameden Ahmedou (Universität Gießen) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Vi a Microsoft Teams.\n\nAbstract\nIn this talk I will report on   a refine d blow up analysis of  finite  energy approximated solutions to the Nire nberg's problem on half  spheres. The later   consists of prescribing u nder minimal boundary  conditions the scalar curvature to be a given func tion. In particular  we give a precise location of blow up points and blo w up rates. Such  an analysis shows that the blow up picture of the Niren berg's problem  on half spheres is far more complicated that in the case of closed  spheres. Indeed besides the combination of interior and bounda ry blow  ups\, there are "non simples blow ups"  for subcritical solutio ns  having zero or  nonzero weak limit. The formation  of such  non si mple  blow ups is governed by a vortex problem\, unveiling an  unexpecte d  connection with  Euler equations in fluid dynamic and mean fields typ e  equations in mathematical physics.\nThis is joint work with Moham ed Ben Ayed (Sfax University).
\nNB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18 000100006\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 14/ END:VEVENT BEGIN:VEVENT SUMMARY:Mario Santilli (University of Augsburg) DTSTART:20210318T130000Z DTEND:20210318T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/15 DESCRIPTION:Title: Regularity of distance functions from arbitra ry closed sets\nby Mario Santilli (University of Augsburg) as part o f Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microso ft Teams.\n\nAbstract\nLet $ \\phi $ be a non-Euclidean uniformly convex n orm. We show that the gradient of an anisotropic $\\phi$-distance function $\\delta^\\phi_K $ from an arbitrary closed subset $K$ of $R^n$ satisfies a local Lipschitz property on the complement of the $\\phi$-cut-locus of K\; namely on $R^n \\setminus (K \\cup Cut^\\phi(K))$. Then we study the g eometric properties of the set points where the distance function is secon d-order pointwise differentiable.  The available known results allow only to conclude that the gradient of $ \\delta^\\phi_K $  is locally Lipschi tz on the interior of $R^n \\setminus (K \\cup Cut^\\phi(K))$\, which migh t be empty even if K is a $C^{​​​1\,\\alpha}​​​$ hypersurface or K is the complementary of a convex body with $C^1 $ boundary.\n

\nNB:This talk is part of the activity of the MIUR Excellence De partment Project MATH@TOV CUP E83C18000100006\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 15/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Caponigro (Università di Roma "Tor Vergata") DTSTART:20210325T130000Z DTEND:20210325T140000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/16 DESCRIPTION:Title: Geometric controllability of the bilinear Schrödi nger equation\nby Marco Caponigro (Università di Roma "Tor Vergata") as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Vi a Microsoft Teams.\n\nAbstract\nWe consider the bilinear Schrödinger equa tion with a discrete-spectrum free Hamiltonian and we present a general me thod for the approximate controllability based on Lie-algebraic control te chniques applied to suitable finite dimensional approximation of the Galer kin-type. Under some regularity assumptions on the Hamiltonians and generi c conditions on the controllability of the finite dimensional Galerkin app roximations we show exact controllability in projection on an arbitrary gi ven number of eigenstates.\n \n\n
\nNB:This talk is part of t he activity of the MIUR Excellence Department Project MATH@TOV CUP E83C180 00100006\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 16/ END:VEVENT BEGIN:VEVENT SUMMARY:Louis Jeanjean (University of Bourgogne Franche-Comté) DTSTART:20210401T120000Z DTEND:20210401T130000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/17 DESCRIPTION:Title: Prescribed norm solutions of Schrödinger equation s with mixed power nonlinearities\nby Louis Jeanjean (University of Bo urgogne Franche-Comté) as part of Analysis Seminar @ Univ. Rome Tor Verga ta\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nIn this talk\, I w ill present some recent results concerning the existence of prescribed nor m solutions in problems where the associated nonlinearity is the sum of tw o powers\, one which is mass-subcritical and one mass-supercritical. This leads to consider a constrained variational problem presenting a so-called convex-concave geometry. The issues of existence\, multiplicity and orbit al stability of solutions will be addressed with a special emphasize on th e cases where the mass-supercritical power is Sobolev critical. \n
\nT he content of this talk is based on some jointed work with J. Jendrej\, T. T. Le and N. Visciglia.\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 17/ END:VEVENT BEGIN:VEVENT SUMMARY:Roberta Ghezzi (Università di Roma "Tor Vergata") DTSTART:20210415T120000Z DTEND:20210415T130000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/18 DESCRIPTION:Title: Regularization of chattering phenomena via bo unded variation controls\nby Roberta Ghezzi (Università di Roma "To r Vergata") as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLectur e held in Via Microsoft Teams.\n\nAbstract\nIn control theory\, chattering refers to fast oscillations of controls\, such as accumulation of switchi ngs in finite time. This behavior is rather typical\, as it is the case fo r the class of single-input control-affine problems\, and may be a serious obstacle to convergence of standard numerical methods to detect optimal s olutions.\n\nWe propose a general regularization procedure\, consisting of penalizing the cost functional with a total variation term. Under appropr iate assumptions of small-time local controllability\, we prove that the o ptimal cost and any optimal solution of the regularized problem converge r espectively to the optimal cost and an optimal solution of the initial pro blem. Our approach is valid for general classes of nonlinear optimal contr ol problems and applies to chattering phenomena appearing in constrained p roblems as well as to switching systems. We also quantify the error in ter ms of the rate of convergence of the sequence of switching times\, for sys tems with regular time-optimal map.\n\nNote: This talk is part o f the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C 18000100006\n\n\n\n___________________________________________________ _____________________________\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 18/ END:VEVENT BEGIN:VEVENT SUMMARY:Aleks Jevnikar (Università di Udine) DTSTART:20210429T120000Z DTEND:20210429T130000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/19 DESCRIPTION:Title: Existence results for super-Liouville equations\nby Aleks Jevnikar (Università di Udine) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract \nWe consider super-Liouville equations on closed surfaces\, which have a variational structure with a strongly-indefinite functional. We obtain the first existence results by making use of min-max methods and bifurcation theory. Joint project with Andrea Malchiodi and Ruijun Wu.\n
\nNB:This talk is part of the activity of the MIUR Excellence Department P roject MATH@TOV CUP E83C18000100006\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 19/ END:VEVENT BEGIN:VEVENT SUMMARY:Margherita Nolasco (Università degli Studi dell'Aquila) DTSTART:20210506T120000Z DTEND:20210506T130000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/20 DESCRIPTION:Title: A variational principle for a charge-normalized so litary wave for the Maxwell-Dirac equations\nby Margherita Nolasco ( Università degli Studi dell'Aquila) as part of Analysis Seminar @ Univ. R ome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nIn th e context of classical field theory\, the solitary wave solutions of the E uler-Lagrange equations describe "extended" particles. The existence of a charge-normalized solitary wave solution of the coupled Maxwell-Dirac equa tions\, describing the spin-1/2 charged particle (electron) with self-inte raction\, has been an open problem for a long time. The first existence result of (not necessarily normalized) solitary waves was given by Est eban\, Georgiev and Séré (Calc.Var. PDE (1996)) by using a variational method\, as critical points of an energy functional which is strongly inde finite and presents a lack of compactness. In this talk we discuss the exi stence of a charge-normalized solitary wave obtained with a different var iational principle inspired by the min-max characterization of eigenvalues of Dirac operators. In particular\, we provide a variational characteri zation of the normalized solitary wave as a minimizer of an effective "re normalized" energy functional.\n\nNote: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006\ n\nMicrosoft Teams Link:\nhttps://teams.microsoft.com/l/meetup-join/19%3a7 f273a2aff1145dfae91372d186b1cd9%40thread.tacv2/1619704157047?context=%7b%2 2Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d 6fea-2e4d-4c35-88e4-99bf4cf68fe9%22%7d\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 20/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone Secchi (Università di Milano Bicocca) DTSTART:20210513T120000Z DTEND:20210513T130000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/21 DESCRIPTION:Title: Concentration phenomena for the Schroedinger-Poiss on system in R^2\nby Simone Secchi (Università di Milano Bicocca) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via M icrosoft Teams.\n\nAbstract\nWe present some recent results obtain in coll aboration with Denis Bonheure (Bruxelles\, Belgium) and Silvia Cingolani ( Bari\, Italy) about a semiclassical analysis for a planar Schroedinger-Poi sson system with potential functions.\n
\nNB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TO V CUP E83C18000100006\n\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 21/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Molica Bisci (Università degli Studi di Urbino) DTSTART:20210520T120000Z DTEND:20210520T130000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/22 DESCRIPTION:Title: Nonsmooth functionals in the Calculus of Variation s\nby Giovanni Molica Bisci (Università degli Studi di Urbino) as par t of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Micr osoft Teams.\n\nAbstract\nIn the last years\, elliptic equations involving a nonsmooth term have attracted several outstanding mathematicians and th e interest towards this kind of problems has grown more and more\, not onl y for their intriguing analytical structure\, but also in view of their ap plications in a wide range of contexts. Motivated by this wide interest in \\end{abstract}\n\n the literature\, the leading purpose of this talk is t o present some recent results on nonsmooth elliptic equations\, mainly rel ated to a wide class of functionals defined through multiple integrals of Calculus of Variations\; see\, among others\, the papers \\cite{arbo0\, ar bo\, arbo2\, ArCar}. Applications to\nquasilinear boundary value problems will be presented and some open problems briefly discussed\; see \\cite{Mo licaBisci} and \\cite[Chapter 8]{MolicaBisciPucci} for related topics.\n\n \\bibitem{arbo0} {\\sc D. Arcoya and L. Boccardo}\, \\emph{A min--max theo rem for multiple integrals of\nthe Calculus of Variations and applications }\, Rend. Mat. Acc. Lincei\, \\textbf{6} (1995)\n29--35.\n\n\\bibitem{arbo } {\\sc D. Arcoya and L. Boccardo}\,\n{\\em Critical points for multiple i ntegrals of Calculus of Variations}\,\n{Arch. Rat. Mech. Anal.} {\\bf134} (1996)\, 249--274.\n\n\\bibitem{arbo2} {\\sc D. Arcoya and L. Boccardo}\, \n{\\em Some remarks on critical point theory for nondifferentiable functi onals}\,\n{Nonlinear Differential Equations and Applications NoDEA} {\\bf6 } (1999)\, 79--100.\n\n\n\\bibitem{ArCar} {\\sc D. Arcoya and J. Carmona} \,\n{\\em A nondifferentiable extension of a theorem\nof Pucci and Serrin and applications}\,\n{J. Differential Equations } {\\bf235} (2007)\, 683- -700.\n\n\\bibitem{MolicaBisci} {\\sc G. Molica Bisci}\,\n\\textit{Local m inima for some functionals in the Calculus of Variations}\,\nsubmitted for publication (2021)\, 1--53.\n\n\\bibitem{MolicaBisciPucci} {\\sc G. Molic a Bisci and P. Pucci}\,\nNonlinear Problems with Lack of Compactness\, De Gruyter Series\nin Nonlinear Analysis and Applications \\textbf{36} (2021) \, i+vii\, 1--266.\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 22/ END:VEVENT BEGIN:VEVENT SUMMARY:Costante Bellettini (University College London (UK)) DTSTART:20210527T120000Z DTEND:20210527T130000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/23 DESCRIPTION:Title: Existence of hypersurfaces with prescribed-mean-cu rvature\nby Costante Bellettini (University College London (UK)) as pa rt of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Mic rosoft Teams.\n\nAbstract\nLet N be a compact Riemannian manifold of dimen sion 3 or higher\, and g a Lipschitz non-negative (or non-positive) functi on on N. We prove that there exists a closed hypersurface M whose mean cur vature attains the values prescribed by g (joint work with Neshan Wickrama sekera\, Cambridge). Except possibly for a small singular set (of codimens ion 7 or higher)\, the hypersurface M is C^2 immersed and two-sided (it ad mits a global unit normal)\; the scalar mean curvature at x is g(x) with r espect to a global choice of unit normal. More precisely\, the immersion i s a quasi-embedding\, namely the only non-embedded points are caused by ta ngential self-intersections: around such a non-embedded point\, the local structure is given by two disks\, lying on one side of each other\, and in tersecting tangentially (as in the case of two spherical caps touching at a point). A special case of PMC (prescribed-mean-curvature) hypersurfaces is obtained when g is a constant\, in which the above result gives a CMC ( constant-mean-curvature) hypersurface for any prescribed value of the mean curvature.\nThe construction of M is carried out largely by means of PDE principles: (i) a minmax for an Allen--Cahn (or Modica-Mortola) energy\, i nvolving a parameter that\, when sent to 0\, leads to an interface from wh ich the desired PMC hypersurface is extracted\; (ii) quasi-linear elliptic PDE and geometric-measure-theory arguments\, to obtain regularity conclus ions for said interface\; (iii) parabolic semi-linear PDE (together with s pecific features of the Allen-Cahn framework)\, to tackle cancellation phe nomena that can happen when sending to 0 the Allen-Cahn parameter.\n\nNote : This talk is part of the activity of the MIUR Department of Excellence P roject MATH@TOV CUP E83C18000100006\n\nLink for the streaming (MS Teams):\ nhttps://teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1145dfae91372d18 6b1cd9%40thread.tacv2/1621517541296?context=%7b%22Tid%22%3a%2224c5be2a-d76 4-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c35-88e4-99bf4 cf68fe9%22%7d\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 23/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesca Carlotta Chittaro (Université de Toulon) DTSTART:20210603T120000Z DTEND:20210603T130000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/24 DESCRIPTION:Title: Hamiltonian approach to sufficient optimality cond itions\nby Francesca Carlotta Chittaro (Université de Toulon) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Micro soft Teams.\n\nAbstract\nThe celebrated Pontryagin Maximum Principle (PMP) provides a (first order) necessary condition for the optimality of trajec tories of optimal control problems. In most cases\, however\, a trajectory satisfying PMP is not optimal. For these reasons\, additional optimality conditions are required.\nIn this context\, Hamiltonian methods are quite effective in establishing sufficient optimality conditions. In this talk\, after a brief review of the main ideas of the general method\, we will fo cus on optimal control problems associated with control-affine dynamics an d costs of the form\n\\[\n\\int_0^T |u(t)| |\\varphi( X(t))| dt\n\\]\n\nCo sts of these form are very common in problems modeling neurobiology\, mech anics and fuel-consumption.\n\nNote: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006\n\nMS Teams Link:\nhttps://teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1145 dfae91372d186b1cd9%40thread.tacv2/1622121687579?context=%7b%22Tid%22%3a%22 24c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c3 5-88e4-99bf4cf68fe9%22%7d\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 24/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Palmurella (ETH Zürich) DTSTART:20210610T120000Z DTEND:20210610T130000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/25 DESCRIPTION:Title: The parametric approach to the Willmore flow\n by Francesco Palmurella (ETH Zürich) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nWe i ntroduce a parametric framework for the study of Willmore gradient flows w hich enables to consider a general class of weak\, energy-level solutions and opens the possibility to study energy quantization and finite-time sin gularities. In this first work we restrict to a small-energy regime and pr ove that\, for small-energy weak immersions\, the Cauchy problem in this c lass admits a unique solution. Joint work with T. Rivière.\n
\n \n NB:This talk is part of the activity of the MIUR Excelle nce Department Project MATH@TOV CUP E83C18000100006\n \n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 25/ END:VEVENT BEGIN:VEVENT SUMMARY:Carina Geldhauser (University of Lund\, Sweden) DTSTART:20211019T140000Z DTEND:20211019T150000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/26 DESCRIPTION:Title: Discrete models for atmospheric turbulence\nby Carina Geldhauser (University of Lund\, Sweden) as part of Analysis Semin ar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbs tract\nn this talk we discuss a family of discrete models for atmospheric turbulence\, often called point vortex models.\n\nPoint vortices provide a n approximation of solutions to generalized surface quasi-geostrophic mode ls\, a family of fractional PDEs which interpolate between 2D Euler equati ons and the more irregular SQG equation.\n\nWe state some of it basic prop erties and see how variational methods and tools from probability theory t ogether can help us to obtain more information about turbulence phenomena. \n\nThe content of this talk is based on work in collaboration with Marco Romito (University of Pisa)\, the presentation tries to avoid technicaliti es and to be accessible to a mixed audience.\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 26/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafael Soriano-Lopez (Universidad Carlos III Madrid) DTSTART:20211123T150000Z DTEND:20211123T160000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/27 DESCRIPTION:Title: Bound and ground states for an elliptic system wit h double criticality\nby Rafael Soriano-Lopez (Universidad Carlos III Madrid) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture he ld in Via Microsoft Teams.\n\nAbstract\nWe will consider a nonlinear ellip tic system in $\\mathbb{​​​​​R}​​​​​^N$.\nThe interes t of this problem is based on the presence of critical power\nn onlinearities and a nonlinear coupling\, possibly critical\, as we ll as\nHardy-type singular potentials. By means of variational methods\, we will\nfocus on the existence of solutions. More precisely\, we shall de rive new\nresults on bound and ground states of the underlying en ergy functional.\nFinally\, we extend our results to the special  case of\n``Schrödinger-Korteweg-de Vries'' coupling type term.\n\nTh is seminar is based on a couple of works in collaboration with\ nEduardo Colorado and Alejandro Ortega (UC3M).\n

\n \ n NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006\n \n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 27/ END:VEVENT BEGIN:VEVENT SUMMARY:Joost Hulshof (Vrije Universiteit Amsterdam) DTSTART:20211130T150000Z DTEND:20211130T160000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/28 DESCRIPTION:Title: Advancing front solutions in a degenerate reaction -diffusion system\nby Joost Hulshof (Vrije Universiteit Amsterdam) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via M icrosoft Teams.\n\nAbstract\nWe are interested in planar travelling wave s olutions of the system\n$$\nu_t=\\varepsilon\\\,\\nabla\\cdot u\\nabla u+u v\,\\quad v_t=\\nabla\\cdot\\nabla u-uv\,\n$$\nwith nonnegative profiles  $U$ and $V$ that satisfy $U(-\\infty)=V(+\\infty)=0$ and $U(\\infty)=V(-\ \infty)=1$.\nThe corresponding solutions have $u\\to1$ and $v\\to0$ as $t\ \to\\infty$.\nAmong these traveling wave profiles there's one with $U\\equ iv0$ on the left and $U>0$ on the right.\nWe discuss its existence and an approach towards its stability analysis\, using a linearisation technique that we developed for the Porous Medium Fischer equation $u_t=(uu_x)_x+u(1 -u)$ (PMF).\nThis is part of an ongoing research project with Michiel Bert sch\, Lorenzo Giacomelli and others\, suggested to us by Mayan Mimura.\nTh e ultimate goal is to show that for small $\\varepsilon>0$ the front solut ions are stable in 1D but unstable in 2D.\nFor now it seems that the resul ts for (PMF) are nontrivial and new.\n

\n \n NB:< i>This talk is part of the activity of the MIUR Excellence Department Proj ect MATH@TOV CUP E83C18000100006\n \n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 28/ END:VEVENT BEGIN:VEVENT SUMMARY:Tien Khai Nguyen (North Carolina State University) DTSTART:20210803T140000Z DTEND:20210803T150000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/29 DESCRIPTION:Title: Differential Game Models of Optimal Debt Managemen t\nby Tien Khai Nguyen (North Carolina State University) as part of An alysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft T eams.\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 29/ END:VEVENT BEGIN:VEVENT SUMMARY:Tien Khai Nguyen (North Carolina State University) DTSTART:20211207T150000Z DTEND:20211207T160000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/30 DESCRIPTION:Title: Differential Game Models of Optimal Debt Managemen t\nby Tien Khai Nguyen (North Carolina State University) as part of An alysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft T eams.\n\nAbstract\nIn this talk\, I will present recent results on game t heoretical formulation of optimal debt management problems in an infinite time horizon with exponential discount\, modeled as a noncooperative inter action between a borrower and a pool of risk-neutral lenders. Here\, the y early income of the borrower is governed by a stochastic process and bankr uptcy instantly occurs when the debt-to-income ratio reaches a threshold. Since the borrower may go bankrupt in finite time\, the risk-neutral lende rs will charge a higher interest rate in order to compensate for this poss ible loss of their investment. Thus\, a "solution" must be understood as a Nash equilibrium\, where the strategy implemented by the borrower represe nts the best reply to the strategy adopted by the lenders\, and conversely . This leads to highly nonstandard optimization process

\n \n NB:This talk is part of the activity of the MIUR Excellenc e Department Project MATH@TOV CUP E83C18000100006\n \n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 30/ END:VEVENT BEGIN:VEVENT SUMMARY:Azahara DelaTorre (Universita' di Roma "La Sapienza") DTSTART:20220208T150000Z DTEND:20220208T160000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/31 DESCRIPTION:Title: The fractional Yamabe problem with singularities\nby Azahara DelaTorre (Universita' di Roma "La Sapienza") as part of An alysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft T eams.\n\nAbstract\nThe so called Yamabe problem in Conformal Geometry cons ists in finding a metric conformal to a given one and which has constant s calar curvature. From the analytic point of view\, this problem becomes a semilinear elliptic PDE with critical (for the Sobolev embedding) power no n-linearity. If we study the problem in the Euclidean space\, allowing the presence of nonzero-dimensional singularities can be transformed into red ucing the non-linearity to a Sobolev-subcritical power. A quite recent not ion of non-local curvature gives rise to a parallel study which weakens th e geometric assumptions giving rise to a non-local semilinear elliptic PDE . \n\nIn this talk\, we will focus on metrics which are singular along non zero-dimensional singularities. In collaboration with Ao\, Chan\, Fontelos \, González and Wei\, we covered the construction of solutions which are singular along (zero and positive dimensional) smooth submanifolds in this fractional setting. This was done through the development of new methods coming from conformal geometry and Scattering theory for the study of non- local ODEs. Due to the limitations of the techniques we used\, the particu lar case of ``maximal’’ dimension for the singularity was not covered. In a recent work\, in collaboration with H. Chan\, we cover this specific dimension constructing and studying singular solutions of critical dimens ion. \n

\n \n NB:This talk is part of the acti vity of the MIUR Excellence Department Project MATH@TOV CUP E83C1800010000 6\n \n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 31/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Augier (CNRS-LAAS\, Toulouse) DTSTART:20220215T150000Z DTEND:20220215T160000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/32 DESCRIPTION:Title: On the use of quasi-static controls and duplicatio n of controls for quantum systems\nby Nicolas Augier (CNRS-LAAS\, Toul ouse) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Microsoft Teams.\n\nAbstract\nIn a first part of the talk\, I will present some geometric techniques allowing to control quantum systems usi ng slowly-varying controls\, in the so-called adiabatic regime. The latter provides strong control results only when the system is driven by at leas t two controls\, which is a strong requirement in practice. The second par t of the talk will be dedicated to an averaging approximation (Rotating Wa ve Approximation) which allows to duplicate controls in this setting.\n

\n \n NB:This talk is part of the activity of th e MIUR Excellence Department Project MATH@TOV CUP E83C18000100006\n \n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 32/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Fidaleo (Università di Roma "Tor Vergata") DTSTART:20220503T140000Z DTEND:20220503T150000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/33 DESCRIPTION:Title: Spectral actions for q-particles and their asympto tic\nby Francesco Fidaleo (Università di Roma "Tor Vergata") as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via Micros oft Teams.\n\nAbstract\nFor spectral actions made of the average number of particles and arising from open systems made of general free $q$-particle s (including Bose\, Fermi and classical ones corresponding to $q=\\pm1$ an d $0$\, respectively) in thermal equilibrium\, we compute the asymptotic e xpansion with respect to the natural cut-off. We treat both relevant situa tions relative to massless and massive particles\, where the natural cut-o ff is $1/\\beta=k_{\\rm B}T$ and $1/\\sqrt{\\beta}$\, respectively. \nWe show that the massless situation enjoys less regularity properties than th e massive one. We also consider the passage to the continuum describing in finitely extended open systems in thermal equilibrium. We briefly discuss the appearance of condensation phenomena occurring for Bose-like $q$-parti cles\, for which $q\\in(0\,1]$\, after passing to the continuum. We also c ompare the arising results for the finite volume situation (discrete spect rum) with the corresponding infinite volume one (continuous spectrum).\n
\n \n NB:This talk is part of the activity of t he MIUR Excellence Department Project MATH@TOV CUP E83C18000100006\n \n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 33/ END:VEVENT BEGIN:VEVENT SUMMARY:Chaona Zhu (Chinese Academy of Sciences and Roma "Tor Vergata") DTSTART:20220517T140000Z DTEND:20220517T150000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/34 DESCRIPTION:Title: Prescribing scalar curvatures: the negative case\nby Chaona Zhu (Chinese Academy of Sciences and Roma "Tor Vergata") as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLecture held in Via M icrosoft Teams.\n\nAbstract\nThe problem of prescribing conformally the sc alar curvature on a closed manifold of negative Yamabe invariant is always solvable\, if the function to be prescribed is strictly negative\, while sufficient and necessary conditions are known in the case that function is non positive. Still in the case of a negative Yamabe invariant\, Rauzy (T rans. Amer. Math. Soc. 1995) showed solvability\, if the function to be pr escribed is not too positive\, as quantified by Aubin-Bismuth (J. Funct. A nal. 1997) later on. In this talk we will review these results variational ly and shed some light on the case\, when Rauzy’s conditions fail. This talk is joint work with Martin Mayer.\n 

\n \n NB:This talk is part of the activity of the MIUR Excellence Department P roject MATH@TOV CUP E83C18000100006\n \n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 34/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Calanchi (Università degli studi di Milano) DTSTART:20220524T140000Z DTEND:20220524T150000Z DTSTAMP:20260404T111000Z UID:AnalysisSeminarRomeTorV/35 DESCRIPTION:Title: Bifurcation of positive solution for a Neumann pro blem with indefinite weights\nby Marta Calanchi (Università degli stu di di Milano) as part of Analysis Seminar @ Univ. Rome Tor Vergata\n\nLect ure held in Via Microsoft Teams.\n\nAbstract\nWe consider eigenvalue probl ems and bifurcation of positive solutions for elliptic equations with inde finite weights and with Neumann boundary conditions. We give complete resu lts concerning the existence and non- existence of positive solutions for the superlinear coercive and non-coercive problems\, showing a surprising complementarity of the respective results.\nJoint work with Bernhard Ruf ( Università degli Studi di Milano).\n

\n \n NB:< i>This talk is part of the activity of the MIUR Excellence Department Proj ect MATH@TOV CUP E83C18000100006\n \n LOCATION:https://stable.researchseminars.org/talk/AnalysisSeminarRomeTorV/ 35/ END:VEVENT END:VCALENDAR