Calculus of Variations and Geometric Measure Theory

A direct approach to an epiperimetric inequality for Free-Boundary problems

Luca Spolaor (UCSD)

created by gelli on 13 Dec 2016

11 jan 2017 -- 17:00   [open in google calendar]

Aula Seminari Dipartimento di Matematica di Pisa


Using a direct approach, we prove a 2-dimensional epiperimetric inequality for the one-phase problem in the scalar and vectorial cases and for the double-phase problem. From this we deduce the $C^{1,α}$ regularity of the free-boundary in the scalar one-phase and double-phase problems, and of the reduced free-boundary in the vectorial case, without any restriction on the sign of the component functions. In this talk I will try to explain the proof of the epiperimetric inequality in the scalar one-phase problem. This is joint work with Bozhidar Velichkov.