Research Group:
Speaker:
Luca Spolaor
Institution:
MIT
Schedule:
Tuesday, January 24, 2017 - 14:00
Location:
A-134
Abstract:
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 $C^{1,\alpha}$ 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.