# Giorgio Tortone: On the regularity of the optimal shapes for a class of integral functionals

**Time: **
Wed 2022-10-26 14.00 - 15.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

**Video link: **
Meeting ID: 921 756 1880

**Participating: **
Giorgio Tortone - University of Pisa

**Abstract:**

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.