On the regularity of the optimal shapes for a class of integral functionals

Date: 2022-11-11

Time: 14:00 - 15:00

Zoom link: https://kva-se.zoom.us/j/9217561880


Giorgio Tortone


The talk deals with the regularity of a free boundary problem arising in the optimization of a class of integral shape functionals. Three variables are involved: two state function u, v and a shape Ω, with u and v satisfying an overdetermined boundary value problem involving the product of their normal derivatives.

The key points of the analysis are a blow-up analysis, involving three blow-ups before finding a homogeneous limit function, and the study of the dimension of the singular set, which requires a new theory for stable solutions of the Bernoulli problem.

These results have been obtained in collaboration with G. Buttazzo, F. Maiale, D. Mazzoleni, and B. Velichkov.