Calculus of Variations and Geometric Measure Theory

Vectorial problems with thin free boundaries

Giorgio Tortone (Università di Pisa)

created by gelli on 05 Nov 2020

11 nov 2020 -- 17:00   [open in google calendar]

online on Microsoft Teams

In order to join the seminar, please fill in the mandatory participation form before November 10th. Further information and instructions will be sent afterwards to the online audience.


The talk deals with recent results obtained in collaboration with D. De Silva on the regularity of free boundaries in vectorial Bernoulli type problems.

The new main point is the analysis of the regular part of the free boundary based on a linearization argument that takes care of the norm of the vector of solutions and that distinguishes appropriately its components. We apply this methodology on the vectorial analogue of the thin free boundary problem introduced by Caffarelli-Roquejoffre-Sire as a realization of a nonlocal version of the classical Bernoulli problem. Time permitting, we discuss the link between this problem and shape optimization problems involving a combination of fractional eigenvalues.