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SUMMARY:Recent applications of quantitative stability to convergence to eq
 uilibrium - Alessio Figalli - ETH Zürich
DTSTART:20161017T140000Z
DTEND:20161017T150000Z
UID:TALK68201@talks.cam.ac.uk
CONTACT:Mikaela Iacobelli
DESCRIPTION:Geometric and functional inequalities play a crucial role in s
 everal PDE problems.\n\nVery recently there has been a growing interest in
  studying the stability for such inequalities. The basic question one want
 s to address is the following:\n\nSuppose we are given a functional inequa
 lity for which minimizers are known. Can we prove\, in some quantitative w
 ay\, that if a function “almost attains the equality” then it is close
  to one of the minimizers?\n\nActually\, in view of applications to PDEs\,
  a even more general and natural question is the following: suppose that a
  function almost solve the Euler-Lagrange equation associated to some func
 tional inequality. Is this function close to one one of the minimizers?\n\
 nWhile in the first case the answer is usually positive\, in the second ca
 se one has to face the presence of bubbling phenomena.\n\nIn this talk I
 ’ll give a overview of these general questions using some concrete examp
 les\, and then present recent applications to some fast diffusion equation
  related to the Yamabe flow.
LOCATION:CMS\, MR13
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