Special Session 93: Local and nonlocal elliptic boundary value problems
Weighted Isoperimetric Inequalities for Manifolds with Double Densities and Applications to PDEs
Francesco Chiacchio
Universita` degli Studi di Napoli Federico II Italy
Co-Author(s): A. Alvino, F. Brock, A. Mercaldo, C. Nitsch, M. R. Posteraro, and C. Trombetti.
Abstract:
We investigate a class of isoperimetric inequalities in R^N characterized by the presence of two different positive weight functions in the volume and surface measures. A central role is played by radial power weights, |x|^a, for which we have solved the isoperimetric problem in many cases. We will present several applications, including Talenti-type estimates for elliptic equations and eigenvalue bounds for Steklov-type problems.