Calculus of Variations and Geometric Measure Theory

A. Figalli

Regularity of interfaces in phase transitions via obstacle problems

created by figalli on 13 Aug 2018
modified by root on 09 Sep 2018



Inserted: 13 aug 2018
Last Updated: 9 sep 2018

Journal: Proceedings ICM 2018
Year: 2018


The aim of this note is to review some recent developments on the regularity theory for the stationary and parabolic obstacle problems.

After a general overview, we present some recent results on the structure of singular free boundary points. Then, we show some selected applications to the generic smoothness of the free boundary in the stationary obstacle problem (Schaeffer's conjecture), and to the smoothness of the free boundary in the one-phase Stefan problem for almost every time.