Calculus of Variations and Geometric Measure Theory

Vectorial free boundary problems

Bozhidar Velichkov (Università di Pisa)

created by vangoethem on 25 Feb 2021

4 mar 2021 -- 15:00   [open in google calendar]

WADE (Webinar in Analysis and Differential Equations)--Rome time


The vectorial Bernoulli problem is a variational free boundary problem involving the Dirichlet energy of a vector-valued function and the measure of its support. It is the vectorial counterpart of the classical one-phase Bernoulli problem, which was first studied by Alt and Caffarelli in 1981.

In this talk, we will discuss some results on the regularity of the vectorial free boundaries obtained in the last years by Caffarelli-Shahgholian-Yeressian, Kriventsov-Lin, Mazzoleni-Terracini-V., and Spolaor-V.. Finally, we will present some new results on the rectifiability of the singular set obtained in collaboration with Guido De Philippis, Max Engelstein and Luca Spolaor.