A Epiperimetric approach to singular points in the Alt-Caffarelli functional

Max Engelstein, MIT
Fine Hall 314

We prove a uniqueness of blowups result for isolated singular points of the free boundary of minimizers to the Alt-Caffarelli functional. The key tool is an epiperimetric inequality, which we prove by means of two Fourier expansions (one on the function and one on its free boundary). This is joint work with Luca Spolaor (Princeton/MIT) and Bozhidar Velichkov (Universite Grenoble Alpes).