preprint

Inserted: 29 feb 2024

Year: 2023

Abstract:

We establish a Talenti-type symmetrization result in the form of mass concentration (i.e. integral comparison) for very general linear nonlocal elliptic problems, equipped with homogeneous Dirichlet boundary conditions. In this framework, the relevant concentration comparison for the classical fractional Laplacian can be reviewed as a special case of our main result, thus generalizing the previous results in 21. Finally, using an implicit time discretization techniques, similar results are obtained for the solutions of Cauchy-Dirichlet nonlocal linear parabolic problems.