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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Recent applications of quantitative stability to c
onvergence to equilibrium - Alessio Figalli - ETH
Zürich
DTSTART;TZID=Europe/London:20161017T150000
DTEND;TZID=Europe/London:20161017T160000
UID:TALK68201AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68201
DESCRIPTION:Geometric and functional inequalities play a cruci
al role in several PDE problems.\n\nVery recently
there has been a growing interest in studying the
stability for such inequalities. The basic questio
n one wants to address is the following:\n\nSuppos
e we are given a functional inequality for which m
inimizers are known. Can we prove\, in some quanti
tative way\, that if a function “almost attains th
e equality” then it is close to one of the minimiz
ers?\n\nActually\, in view of applications to PDEs
\, a even more general and natural question is the
following: suppose that a function almost solve t
he Euler-Lagrange equation associated to some func
tional inequality. Is this function close to one o
ne of the minimizers?\n\nWhile in the first case t
he answer is usually positive\, in the second case
one has to face the presence of bubbling phenomen
a.\n\nIn this talk I’ll give a overview of these g
eneral questions using some concrete examples\, an
d then present recent applications to some fast di
ffusion equation related to the Yamabe flow.
LOCATION:CMS\, MR13
CONTACT:Mikaela Iacobelli
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