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SUMMARY:Stable Free Boundaries in Dimension 3: Bernoulli and Allen--Cahn
DTSTART:20251003T141500
DTSTAMP:20260510T202409Z
UID:40c50505bcfcfea164ad5308d22dac8113cb97e3a6f2e63996d53650
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Xavier Fernandez-Real (EPFL-AMCV)\nAbstract:\n \nIn this 
 talk\, I will present our recent work on the classification of global stab
 le solutions to the Bernoulli problem in $\\mathbb R^3$. In particular\, t
 his yields local universal curvature bounds for the free boundary for the 
 local problem.\n\nBy means of this result\, we prove the free boundary All
 en--Cahn stability conjecture in dimension 3: global stable solutions to t
 he free boundary analogue of the Allen--Cahn equation are one dimensional 
 in dimension 3. This solves the long-standing De Giorgi conjecture in the 
 free boundary case.
LOCATION:MA B1 11 https://plan.epfl.ch/?room==MA%20B1%2011
STATUS:CONFIRMED
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