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SUMMARY:Alessio Figalli (ETH Zurich/FIM)
DTSTART:20200702T140000Z
DTEND:20200702T153000Z
DTSTAMP:20260422T225926Z
UID:Sissa-Ictp/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Sissa-Ictp/1
 /">Generic Regularity in Obstacle Problems</a>\nby Alessio Figalli (ETH Zu
 rich/FIM) as part of Joint SISSA-ICTP Webinar Colloquium\n\n\nAbstract\nTh
 e classical obstacle problem consists of finding the equilibrium position 
 of an elastic membrane whose boundary is held fixed and which is constrain
 ed to lie above a given obstacle. By classical results of Caffarelli\, the
  free boundary is $C^\\infty$ outside a set of singular points. Explicit e
 xamples show that the singular set could be in general $(n-1)$-dimensional
  that is\, as large as the regular set. In a recent paper with Ros-Oton an
 d Serra we show that\, generically\, the singular set has zero $\\mathcal{
 H}^{n-4}$ measure (in particular\, it has codimension 3 inside the free bo
 undary)\, solving a conjecture of Schaeffer in dimension $n \\leq 4$. The 
 aim of this talk is to give an overview of these results.\n\nThe talk will
  be followed by a question/answer session.\n\nPre-registration is required
  at the following url: https://sissa-it.zoom.us/webinar/register/WN_ca93G0
 1TQ6eO0zn99mkp-g\nAfter registering\, you will receive a confirmation emai
 l containing information about joining the webinar.\n
LOCATION:https://researchseminars.org/talk/Sissa-Ictp/1/
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