On the regularity of the optimal shapes for a class of integral functionals
Geometric Aspects of Nonlinear Partial Differential Equations
11 November 14:00 - 15:00
Giorgio Tortone - University of Pisa
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.
KTH Royal Institute of Technology
University of Turin