Analysis and PDE Seminar Series
A Epiperimetric inequality for singular points in the Alt-Caffarelli functional
ABSTRACT: We study singular points of the free boundary of minimizers to the Alt-Caffarelli functional. In particular, we show that blowups are unique (and occur at a power rate) at points at which at least one of the blowups is rotationally symmetric. The key tool is an epiperimetric inequality, which we prove by means of two Fourier expansions (on the function and one on its free boundary). This is joint work with Luca Spolaor (Princeton/MIT) and Bozhidar Velichkov (Universite Grenoble Alpes).
Tuesday, September 26, 2017
Stratton Hall 304