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SUMMARY:Alessio Figalli (ETH Zurich/FIM)
DTSTART;VALUE=DATE-TIME:20200702T140000Z
DTEND;VALUE=DATE-TIME:20200702T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T032507Z
UID:Sissa-Ictp/1
DESCRIPTION:Title: Generic Regularity in Obstacle Problems\nby Alessio Fig
alli (ETH Zurich/FIM) as part of Joint SISSA-ICTP Webinar Colloquium\n\n\n
Abstract\nThe classical obstacle problem consists of finding the equilibri
um position of an elastic membrane whose boundary is held fixed and which
is constrained to lie above a given obstacle. By classical results of Caff
arelli\, the free boundary is $C^\\infty$ outside a set of singular points
. Explicit examples 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 and Serra we show that\, generically\, the singular set has zero
$\\mathcal{H}^{n-4}$ measure (in particular\, it has codimension 3 inside
the free boundary)\, solving a conjecture of Schaeffer in dimension $n \\
leq 4$. The aim of this talk is to give an overview of these results.\n\nT
he talk will be followed by a question/answer session.\n\nPre-registration
is required at the following url: https://sissa-it.zoom.us/webinar/regist
er/WN_ca93G01TQ6eO0zn99mkp-g\nAfter registering\, you will receive a confi
rmation email containing information about joining the webinar.\n
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