Seminar series
Date
Mon, 17 Feb 2025
16:30
16:30
Location
L4
Speaker
Xavier Fernandez-Real
Organisation
EPFL
In this talk, we present a forthcoming work on the classification of global stable solutions to the Bernoulli problem in $\mathbb R^3$. In particular, this yields local universal curvature bounds for the free boundary for the local problem.
By means of this result, we prove the free boundary Allen--Cahn stability conjecture in dimension 3: global stable solutions to the free boundary analogue of the Allen--Cahn equation are one dimensional in dimension 3. This solves a long-standing conjecture in the free boundary case.