BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Camillo De Lellis (IAS\, Princeton)
DTSTART:20200415T200000Z
DTEND:20200415T210000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/1
DESCRIPTION:Title: Flows of vector fields: classical and modern\nby Camillo De Lel
lis (IAS\, Princeton) as part of Rio de Janeiro webinar on analysis and pa
rtial differential equations\n\n\nAbstract\nConsider a (possibly time-depe
ndent) vector field $v$ on the Euclidean space. The classical Cauchy-Lipsc
hitz (also named Picard-Lindel\\"of) Theorem states that\, if the vector f
ield $v$ is Lipschitz in space\, for every initial datum $x$ there is a un
ique trajectory $\\gamma$ starting at $x$ at time $0$ and solving the ODE
$\\dot{\\gamma} (t) = v (t\, \\gamma (t))$. The theorem looses its validit
y as soon as $v$ is slightly less regular. However\, if we bundle all traj
ectories into a global map allowing $x$ to vary\, a celebrated theory put
forward by DiPerna and Lions in the 80es show that there is a unique such
flow under very reasonable conditions and for much less regular vector fie
lds. A long-standing open question is whether this theory is the byproduct
of a stronger classical result which ensures the uniqueness of trajectori
es for {\\em almost every} initial datum. I will give a complete answer to
the latter question and draw connections with partial differential equati
ons\, harmonic analysis\, probability theory and Gromov's $h$-principle.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo A. Gomes (KAUST)
DTSTART:20200422T120000Z
DTEND:20200422T130000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/2
DESCRIPTION:Title: A mean-field price model\nby Diogo A. Gomes (KAUST) as part of
Rio de Janeiro webinar on analysis and partial differential equations\n\n\
nAbstract\nWe propose a mean-field game model for the price formation of a
commodity whose production is subjected to deterministic or random fluctu
ations. Agents seek to minimize their average cost by choosing their tradi
ng rates with a price that is characterized by a balance between supply an
d demand. In the deterministic case\, we establish the existence of a solu
tion under general conditions and give a full characterization. In the sto
chastic case\, we show that\, for linear dynamics and quadratic costs\, th
e optimal trading rates are determined in feedback form. Hence\, the price
arises as the solution to a stochastic differential equation\, whose coef
ficients depend on the solution of a system of ordinary differential equat
ions.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristiana De Filippis (Oxford)
DTSTART:20200429T130000Z
DTEND:20200429T140000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/3
DESCRIPTION:Title: Vectorial problems: sharp Lipschitz bounds and borderline regularit
y\nby Cristiana De Filippis (Oxford) as part of Rio de Janeiro webinar
on analysis and partial differential equations\n\n\nAbstract\nFor the abs
tract of Cristiana's talk\, please use the following link: \n\nhttps://dri
ve.google.com/open?id=1eU6lWvs808FKxdqswC2x3JPJ2jEmMgFz\n\nTo join the web
inar\, use the following information:\n\nLink:\n\nhttps://puc-rio.zoom.us/
j/94917916635?pwd=NWplK0FjZHNldVRXSmcxSnFwdVg0QT09\n\nMeeting ID: 949 1791
6635\nPassword: 085148\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatiana Toro (U. Washington)
DTSTART:20200514T180000Z
DTEND:20200514T190000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/4
DESCRIPTION:Title: Elliptic measure and the geometry of domains in Euclidean space
\nby Tatiana Toro (U. Washington) as part of Rio de Janeiro webinar on ana
lysis and partial differential equations\n\n\nAbstract\nIn this talk we wi
ll discuss the correspondence between the properties of the solutions of a
class of PDEs and the geometry of sets in Euclidean space. In particular
we will examine the relationship between the behavior of the elliptic meas
ure of a certain class divergence form uniformly elliptic operators on a d
omain and the structure of its boundary. This work mixes elements of geome
tric measure theory\, free boundary regularity problems and harmonic analy
sis.\n\nTo join Prof. Tatiana's talk\, please use the following link and i
nformation:\n\nhttps://puc-rio.zoom.us/j/402375411?pwd=N05uYWVBOGMzRm4yU21
kSjBjYVRVUT09\n\nMeeting ID: 402 375 411\nPassword: 084011\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Mingione (University of Parma)
DTSTART:20200507T140000Z
DTEND:20200507T150000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/5
DESCRIPTION:Title: Gradient estimates\nby Giuseppe Mingione (University of Parma)
as part of Rio de Janeiro webinar on analysis and partial differential equ
ations\n\n\nAbstract\nI am going to give a review of gradient estimates fo
r solutions to nonlinear elliptic and parabolic equations\, with special e
mphasis on Nonlinear Potential Theory. Non-uniformly elliptic problems wil
l also be treated.\n\nTo access the seminar\, please use the following inf
ormation:\n\nhttps://zoom.us/j/96230784442?pwd=Um9VVzdnTGpaVzNjeHNyd3oyR25
VUT09\n\nMeeting ID: 962 3078 4442\nPassword: 045854\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susanna Terracini (U. Torino)
DTSTART:20200521T150000Z
DTEND:20200521T160000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/6
DESCRIPTION:Title: Segregation\, interaction of species and related free boundary prob
lems.\nby Susanna Terracini (U. Torino) as part of Rio de Janeiro webi
nar on analysis and partial differential equations\n\n\nAbstract\nPartial
differential equations are often used to describe physical laws governing
a complicated system in a confined space with relatively simpler behaviour
on the boundary. Thus\, reaction-diffusion systems with strong interacti
on terms appear in many multi-species physical problems as well as in popu
lation dynamics\, chemistry and material science. The qualitative properti
es of the solutions and their limiting profiles in different regimes will
be considered\, as well as the interfaces.\n\nTo join Prof. Terracini's le
cture\, please use the following information:\n\nhttps://puc-rio.zoom.us/j
/99546616886?pwd=NHcvM1BXZ3hqNmI5R0YybkFmZmE4QT09\n\nMeeting ID: 995 4661
6886\nPassword: 046379\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filomena Pacella (U. Roma\, Sapienza)
DTSTART:20200528T130000Z
DTEND:20200528T140000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/7
DESCRIPTION:Title: Critical exponents for a class of fully nonlinear equations\nby
Filomena Pacella (U. Roma\, Sapienza) as part of Rio de Janeiro webinar o
n analysis and partial differential equations\n\n\nAbstract\nWe consider a
class of radial fully nonlinear equations involving the extremal Pucci's
operators and power nonlinearities.\nFor such equations some critical expo
nents were introduced by P.Felmer and A.Quaas in 2003\, motivated by the s
tudy of positive entire radial solutions.\nIn the first part of the talk I
will discuss the role and properties of such exponents and its relation w
ith concentration phenomena and energy invariance.\nIn the second part I w
ill present an alternative proof of the existence and uniqueness of these
critical exponents\, entirely based on the study of an associated quadrati
c dynamical system. This approach also allows to get in a unified and simp
le way new existence and classification results for singular solutions as
well as to prove that the same critical exponents give a threshold for the
existence or nonexistence of positive radial solutions for the Dirichlet
problem in exterior domains. This last result was recently proved by G.Ga
lise\, A.Iacopetti and F. Leoni (2019) with a different proof.\nThe result
s presented are contained in several joint papers with I.Birindelli\, G.Ga
lise\, F.Leoni\, L.Maia\, G.Saller Nornberg.\n\nTo join Prof. Pacella's ta
lk\, please use the following information.\n\nLink to join the talk:\nhttp
s://puc-rio.zoom.us/j/91799849377?pwd=bjU4MkpMdC9sWit3bGJQNTBQcnY3UT09\n\n
Meeting ID: 917 9984 9377\nPassword: 801822\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariana Smit Vega Garcia (Western Washington University)
DTSTART:20200612T170000Z
DTEND:20200612T180000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/8
DESCRIPTION:Title: Regularity of almost minimizers with free boundary\nby Mariana
Smit Vega Garcia (Western Washington University) as part of Rio de Janeiro
webinar on analysis and partial differential equations\n\n\nAbstract\nWe
study almost minimizer for functionals which yield a free boundary\, as in
the work of Alt-Caffarelli and Alt-Caffarelli-Friedman. The almost minimi
zing property can be understood as the defining characteristic of a minimi
zer in a problem which explicitly takes noise into account. In this talk\,
we discuss the regularity of almost minimizers to energy functionals with
variable coefficients. This is joint work with Guy David\, Max Engelstein
& Tatiana Toro.\n\nTo join Mariana's webinar\, please use the following i
nformation:\n\nLink to joni Mariana's talk:\nhttps://puc-rio.zoom.us/j/947
72587702?pwd=MHFJWjRFZ244eXYrN0ZkWFNRMElpZz09\n\nMeeting ID: 947 7258 7702
\nPassword: 261257\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hugo Tavares (Instituto Superior Técnico\, IST-Lisbon)
DTSTART:20200618T150000Z
DTEND:20200618T160000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/9
DESCRIPTION:Title: Behavior near criticality of sign-changing solutions to the Lane-Em
den equation with Dirichlet and Neumann boundary conditions\nby Hugo T
avares (Instituto Superior Técnico\, IST-Lisbon) as part of Rio de Janeir
o webinar on analysis and partial differential equations\n\n\nAbstract\nIn
this talk we will be concerned with several recent results on the classic
al Lane-Emden equation in a bounded domain\, with either Dirichlet or Neum
ann boundary conditions.\nIn the first part of the talk\, for radial solut
ions and in the case of the ball in dimension 3 or higher\, we provide sha
rp rates and constants describing the asymptotic behavior (as we approach
the Sobolev critical exponent) of all local minima and maxima of the solut
ions\, as well as its derivative at roots. As corollaries\, we complement
a known asymptotic approximation of the Dirichlet nodal solution in terms
of a tower of bubbles and present a similar formula for the Neumann proble
m.\nIn the second part or the talk we analyse the nonradial case with Neum
ann boundary conditions\, namely the existence (and symmetry) of least ene
rgy solutions and their dependence on the exponent of the nonlinearity up
to the Sobolev critical exponent\, discussing also the slightly supercriti
cal case.\nThe talk is based on joint works with Alberto Saldaña\, Angela
Pistoia and Massimo Grossi.\n\nTo join Hugo's talk\, please use the follo
wing information:\n\nLink to join Hugo's talk:\nhttps://puc-rio.zoom.us/j/
96415145570?pwd=TERzRmp1Z2RyU2x6OU92dFdHUnBmZz09\n\nMeeting ID: 964 1514 5
570\nPassword: 125966\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yehuda Pinchover (Technion)
DTSTART:20200813T130000Z
DTEND:20200813T140000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/10
DESCRIPTION:Title: How large can Hardy-weight be?\nby Yehuda Pinchover (Technion)
as part of Rio de Janeiro webinar on analysis and partial differential eq
uations\n\n\nAbstract\nIn the first part of the talk we will discuss the e
xistence of optimal Hardy-type inequalities with 'as large as possible' Ha
rdy-weight for a general second-order elliptic operator defined on noncomp
act Riemannian manifolds and discrete graphs\, while the second part of th
e talk will be devoted to a sharp answer to the question: "How large can H
ardy-weight be?"\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noemi Wolanski (U. Buenos Aires)
DTSTART:20200827T140000Z
DTEND:20200827T150000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/11
DESCRIPTION:Title: Fractional heat equations with memory in $\\R^N$. Behavior in $L^p
(\\R^N)$\nby Noemi Wolanski (U. Buenos Aires) as part of Rio de Janeir
o webinar on analysis and partial differential equations\n\n\nAbstract\nTo
access the abstract of Prof. Noemi Wolanski's talk\, please\, use the fol
lowing link:\n\nhttps://www.dropbox.com/s/zb8tan4j0fk1clm/abstract_wolansk
i.pdf?dl=0\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria J. Esteban (CEREMADE)
DTSTART:20200917T130000Z
DTEND:20200917T140000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/12
DESCRIPTION:Title: Magnetic interpolation inequalities\nby Maria J. Esteban (CERE
MADE) as part of Rio de Janeiro webinar on analysis and partial differenti
al equations\n\n\nAbstract\nIn this talk I will present various results co
ncerning interpolation inequalities\, best constants and information about
the extremal functions involving Schrödinger magnetic operators in dimen
sions 1\, 2 and 3. The particular\, and physical interesting\, cases of co
nstant and of Aharonov-Bohm magnetic fields will be discussed in detail.\n
\nThese works have been made in collaboration with D. Bonheure\, J. Dolbea
ult\, A. Laptev and M. Loss.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Allen (Brigham Young U.)
DTSTART:20200924T160000Z
DTEND:20200924T170000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/13
DESCRIPTION:Title: A boundary Harnack principle for equations with nonzero right hand
side\nby Mark Allen (Brigham Young U.) as part of Rio de Janeiro webi
nar on analysis and partial differential equations\n\n\nAbstract\nThe boun
dary Harnack principle allows one to compare the behavior of two harmonic
solutions when they both vanish on the boundary. This principle has proven
useful in PDE\, harmonic analysis\, and free boundary problems. In this t
alk I will review the principle and some of its applications. I will then
introduce a new boundary Harnack principle for functions whose Laplacian h
as nonzero right hand sides. This new principle has applications to Hele-S
haw flow as well as free boundary problems. I will also show how we have r
ecently proven this result for fully nonlinear equations as well as the p-
Laplacian. This is joint work with Dennis Kriventsov and Henrik Shahgholia
n.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Maggi (UT Austin)
DTSTART:20201009T160000Z
DTEND:20201009T170000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/14
DESCRIPTION:Title: Symmetry of Plateau Surfaces and the Moving Planes Method with Sin
gularities\nby Francesco Maggi (UT Austin) as part of Rio de Janeiro w
ebinar on analysis and partial differential equations\n\n\nAbstract\nBy em
ploying the method of moving planes in a novel way we extend some classica
l symmetry and rigidity results for smooth minimal surfaces to surfaces th
at have singularities of the sort typically observed in soap films. This i
s a joint work with Jacob Bernstein at Johns Hopkins University.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Porretta (Roma Tor Vergata)
DTSTART:20201016T130000Z
DTEND:20201016T140000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/16
DESCRIPTION:Title: Mean field games: a bridge between Hamilton-Jacobi and transport-d
iffusion equations\nby Alessio Porretta (Roma Tor Vergata) as part of
Rio de Janeiro webinar on analysis and partial differential equations\n\n\
nAbstract\nMean field game theory was developed since 2006 by J.‑M. Lasr
y and P.‑L. Lions in order to adapt the concept of Nash equilibria to di
fferential games with infinitely many players. In this context\, the value
function of any small player depends on the distribution law of the dynam
ical state of the system. This model leads to systems of PDEs coupling Ham
ilton–Jacobi with Fokker–Planck (or continuity) equations. In this tal
k I will describe some features of mean field game systems and their conne
ction with optimal control and optimal transport\, pointing out the role p
layed by weak solutions\, renormalized formulations\, convex analysis and
adjoint methods.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Héctor Chang-Lara (CIMAT)
DTSTART:20201113T160000Z
DTEND:20201113T170000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/17
DESCRIPTION:Title: Eikonal vs. Brownian: Regularity for the solution of an equation w
ith gradient constraint.\nby Héctor Chang-Lara (CIMAT) as part of Rio
de Janeiro webinar on analysis and partial differential equations\n\n\nAb
stract\nTwo controllers are in charge of steering a spaceship in some doma
in Omega. The first controller wants to spend as much time as possible exp
loring Omega while the second wants to get out of it as quickly as possibl
e. The first controller determines minute by minute whether the ship is mo
ving by a Brownian motion or with constant speed\, in which case it is the
second controller who chooses the direction. Under these instructions\, d
etermining the optimal strategies for each player leads us to solve the eq
uation $\\min (-\\Delta u\, |Du|) = 1$ which has several interesting chara
cteristics. Among them is the presence of a free boundary which separates
the regions where a Poisson or an Eikonal equation is satisfied. In a rece
nt collaboration with Edgard Pimentel (PUC-Rio) we showed that the solutio
ns are Lipschitz continuous and that $|Du|$ is continuous\, even though th
e gradient is discontinuous in numerous examples. This problem is a simpli
fication of interesting models in financial mathematics related with the o
ptimal strategy for the payment of dividends from multiple insurances.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edriss S. Titi (U. Cambridge\, Texas A&M U. and Weizmann Institute
of Science)
DTSTART:20201127T140000Z
DTEND:20201127T150000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/18
DESCRIPTION:Title: Recent Advances Concerning the Navier-Stokes and Euler Equations\nby Edriss S. Titi (U. Cambridge\, Texas A&M U. and Weizmann Institute
of Science) as part of Rio de Janeiro webinar on analysis and partial diff
erential equations\n\n\nAbstract\nIn this talk I will discuss some recent
progress concerning the Navier-Stokes and Euler equations of incompressibl
e fluid. In particular\, issues concerning the lack of uniqueness using th
e convex integration machinery and their physical relevance. Moreover\, I
will show the universality of the critical $1/3$ H\\"older exponent\, conj
ectured by Onsager for the preservation of energy in Euler equations\, by
extending the Onsager conjecture for the preservation of generalized entro
py in general conservation laws. In addition\, I will present a blow-up c
riterion for the 3D Euler equations based on a class of inviscid regulariz
ation for these equations and the effect of physical boundaries on the pot
ential formation of singularity.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:YanYan Li (Rutgers U.)
DTSTART:20201203T150000Z
DTEND:20201203T160000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/19
DESCRIPTION:Title: Gradient estimates for the insulated conductivity problem\nby
YanYan Li (Rutgers U.) as part of Rio de Janeiro webinar on analysis and p
artial differential equations\n\n\nAbstract\nIn this talk\, we discuss the
insulated conductivity problem with multiple inclusions embedded in a bou
nded domain in $n$-dimensional Euclidean space. The gradient of a solution
may blow up as two inclusions approach each other. The optimal blow up ra
te was known in dimension $n=2$. It was not known whether the established
upper bound of the blow up rates in higher dimensions were optimal. We ans
wer this question by improving the previously known upper bound of the bl
ow up rates in dimension $n>2$. This is a joint work with Zhuolun Yang.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irene Fonseca (Carnegie Mellon University)
DTSTART:20210305T150000Z
DTEND:20210305T160000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/20
DESCRIPTION:Title: Phase Transitions in Heterogeneous Media: Equilibria and Geometric
Flows\nby Irene Fonseca (Carnegie Mellon University) as part of Rio d
e Janeiro webinar on analysis and partial differential equations\n\n\nAbst
ract\nA variational model in the context of the gradient theory for fluid-
fluid phase transitions with small scale heterogeneities is studied. In th
e case where the scale of the small homogeneities is of the same order of
the scale governing the phase transition\, the interaction between homogen
ization and the phase transitions process leads to an anisotropic interfac
ial energy.\n\nThe underlying gradient flow provides unconditional converg
ence results for an Allen-Cahn type bi-stable reaction diffusion equation
in a periodic medium. The limiting dynamics are given by an analog for ani
sotropic mean curvature flow\, of the formulation due to Ken Brakke. As an
essential ingredient in the analysis\, an explicit expression for the eff
ective surface tension\, which dictates the limiting anisotropic mean curv
ature\, is obtained.\n\nThis is joint work with Riccardo Cristoferi (Radbo
ud University\, The Netherlands)\, Adrian Hagerty\, Cristina Popovici\, Ru
stum Choksi (McGill)\, Jessica Lin (McGill)\, and Raghavendra Venkatraman
(CMU).\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Herbert Koch (Mathematisches Institut\, U. Bonn)
DTSTART:20210318T140000Z
DTEND:20210318T150000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/21
DESCRIPTION:Title: Sobolev regularity for the infinity Laplace equation\nby Herbe
rt Koch (Mathematisches Institut\, U. Bonn) as part of Rio de Janeiro webi
nar on analysis and partial differential equations\n\n\nAbstract\nThe infi
nity Laplace equation is a very degenerate elliptic equation. I report on
Sobolev regularity of $|Du|^a$\, both for solutions to the homogeneous and
the inhomogeneous equation in 2d. This is joint work with Yi Ru-Ya Zhang
and Yuan Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvia Serfaty (CIMS\, NYU)
DTSTART:20210409T140000Z
DTEND:20210409T150000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/22
DESCRIPTION:Title: Mean-Field limits of Coulomb-type dynamics\nby Sylvia Serfaty
(CIMS\, NYU) as part of Rio de Janeiro webinar on analysis and partial dif
ferential equations\n\n\nAbstract\nWe consider a system of $N$ particles e
volving according to the gradient flow of their Coulomb or Riesz interacti
on\, or a similar conservative flow\, and possible added random diffusion.
By Riesz interaction\, we mean inverse power $s$ of the distance. We pres
ent a convergence result as $N$ tends to infinity to the expected limiting
mean field evolution equation. We also discuss the derivation of Vlasov-P
oisson from newtonian dynamics in the monokinetic case\, as well as relate
d results for Ginzburg-Landau vortex dynamics.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabrielle S. Nornberg (Universidade de São Paulo (ICMC-USP))
DTSTART:20210507T140000Z
DTEND:20210507T150000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/23
DESCRIPTION:Title: Qualitative properties of Lane-Emden type systems\nby Gabriell
e S. Nornberg (Universidade de São Paulo (ICMC-USP)) as part of Rio de Ja
neiro webinar on analysis and partial differential equations\n\n\nAbstract
\nIn this talk we discuss some qualitative properties of Lane-Emden type s
ystems and their applications to existence and nonexistence of solutions.\
n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrzej Święch (Georgia Institute of Technology)
DTSTART:20210422T140000Z
DTEND:20210422T150000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/24
DESCRIPTION:Title: Singular perturbations and optimal control of stochastic systems i
n infinite dimension\nby Andrzej Święch (Georgia Institute of Techno
logy) as part of Rio de Janeiro webinar on analysis and partial differenti
al equations\n\n\nAbstract\nWe will discuss a stochastic optimal control p
roblem for a two scale system driven by an infinite dimensional stochastic
differential equation which consists of ''slow'' and ''fast'' components.
We will consider a rather general case where the evolution is given by an
abstract semilinear stochastic differential equation with nonlinear depen
dence on the controls. We will present a PDE approach to the problem based
on the theory of viscosity solutions in Hilbert spaces. This approach all
ows to prove that as the speed of the fast component goes to infinity\, th
e value functions of the optimal control problems converge to the viscosit
y solution of a reduced effective equation. Our results generalize to the
infinite dimensional case the finite dimensional results of Alvarez and Ba
rdi and complement recent results in Hilbert spaces obtained by Guatteri a
nd Tessitore.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabella Ianni (Sapienza Università di Roma)
DTSTART:20210521T140000Z
DTEND:20210521T150000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/25
DESCRIPTION:Title: Radial and non-radial solutions for the Lane-Emden problem in the
disk\nby Isabella Ianni (Sapienza Università di Roma) as part of Rio
de Janeiro webinar on analysis and partial differential equations\n\n\nAbs
tract\nWe discuss sharp asymptotic analysis results on radial solutions of
the Lane-Emden problem in the disk\, which in particular lead to a Morse
index formula. \nAs a consequence we can prove the existence of new unexpe
cted solutions. The talk is based on results mainly contained in [ADI]\, [
IS]\, [GI] and [DIP].\n\n[ADI] A. Amadori\, F. De Marchis\, I. Ianni\, Mor
se index computation for radial solutions of the Henon problem in the disk
\, preprint\n\n[IS] I. Ianni\, A. Saldana\, Sharp asymptotic behavior of r
adial solutions of some planar semilinear elliptic problems\, preprint\n\n
[GI] I. Ianni\, F. Gladiali\, Quasi-radial solutions for the Lane-Emden pr
oblem in the ball\, NoDEA 27 (2) (2020)\n\n[DIP] F. De Marchis\, I. Ianni\
, F. Pacella\, Exact Morse index computation for nodal radial solutions of
Lane-Emden problems\, Mathematische Annalen 367 (2017)\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego R. Moreira (Universidade Federal do Ceará)
DTSTART:20210618T140000Z
DTEND:20210618T150000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/26
DESCRIPTION:Title: Up to the boundary gradient estimates for solutions to nonlinear f
ree boundary problems with unbounded measurable ingredients\nby Diego
R. Moreira (Universidade Federal do Ceará) as part of Rio de Janeiro webi
nar on analysis and partial differential equations\n\n\nAbstract\nIn this
talk\, we discuss recent advances on up to the boundary gradient estimates
for viscosity solutions of free boundary problems governed by fully nonli
near and quasilinear equations with unbounded coefficients. We present the
new Inhomogeneous Pucci Barriers as new elements for the proof. If time
permits\, we discuss some of the main steps in the proof\, namely\, the t
race estimate of the solution on the points of the fixed boundary that pro
jects nontangentially over the free boundary. These methods are inspired b
y some ideas of Carlos Kenig in Harmonic Analysis.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannick Sire (Johns Hopkins U.)
DTSTART:20210715T140000Z
DTEND:20210715T150000Z
DTSTAMP:20260404T094701Z
UID:RJWAPDE/27
DESCRIPTION:Title: Blow-up solutions via parabolic gluing\nby Yannick Sire (Johns
Hopkins U.) as part of Rio de Janeiro webinar on analysis and partial dif
ferential equations\n\n\nAbstract\nWe will present some recent results on
the construction of blow-up solutions for critical parabolic problems of g
eometric flavor. Initiated in the recent years\, the inner/outer parabolic
gluing is a very versatile parabolic version of the well-known Lyapunov-S
chmidt reduction in elliptic PDE theory. The method allows to prove rigoro
usly some formal matching asymptotics (if any available) for several PDEs
arising in porous media\, geometric flows\, etc….I will give an overview
of the strategy and will present several applications to (variations of)
the harmonic map flow\, Yamabe flow and Yang-Mills flow. I will also prese
nt some open questions.\n
LOCATION:https://stable.researchseminars.org/talk/RJWAPDE/27/
END:VEVENT
END:VCALENDAR