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SUMMARY:Joaquim Serra (ETH Zürich)
DTSTART:20200616T131500Z
DTEND:20200616T141500Z
DTSTAMP:20260423T003300Z
UID:OSAnaProb/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSAnaProb/5/
 ">The singular set in the obstacle problem</a>\nby Joaquim Serra (ETH Zür
 ich) as part of Leipzig Oberseminar Analysis - Probability\n\n\nAbstract\n
 The obstacle problem arises in several important physical models. We will 
 present some recent work in collaboration with A. Figalli and X. Ros-Oton 
 on the structure of the singular set for this problem.\n\nWe will start in
 troducing some rather recent tools for the analysis of singularities in th
 e obstacle problem\, which are complementary to the classical theory of Ca
 ffarelli. These tools exploit a useful connection between singularities of
  the obstacle problem and solutions of the so-called thin obstacle problem
 .\n\nWith careful enough analysis\, we are able to achieve a precise under
 standing of the behavior of solutions near "generic" singularities.\n\nIn 
 particular we prove that the free boundary is generically smooth in dimens
 ions 3 and 4\, while in higher dimensions the singular set has\, generical
 ly\, co-dimension 3 inside the free boundary.\n
LOCATION:https://researchseminars.org/talk/OSAnaProb/5/
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