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SUMMARY:Alessio Figalli (ETH Zurich\, Switzerland)
DTSTART:20201203T163000Z
DTEND:20201203T173000Z
DTSTAMP:20260423T040041Z
UID:SIAM-PDE/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SIAM-PDE/6/"
 >Generic regularity in obstacle problems</a>\nby Alessio Figalli (ETH Zuri
 ch\, Switzerland) as part of Seminar In the Analysis and Methods of PDE (S
 IAM PDE)\n\n\nAbstract\nThe classical obstacle problem consists of finding
  the equilibrium position of an elastic membrane whose boundary is held fi
 xed and constrained to lie above a given obstacle. By classical results of
  Caffarelli\, the free boundary is smooth outside a set of singular points
 . Explicit examples show that the singular set could be in general (n-1)-d
 imensional — that is\, as large as the regular set. In a recent paper wi
 th Ros-Oton and Serra we show that\, generically\, the singular set has co
 dimension 3 inside the free boundary\, solving a conjecture of Schaeffer i
 n dimension $n\\leq 4$. This talk aims to give an overview of these result
 s.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/6/
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