Special Session 103: Elliptic, parabolic problems and functional inequalities

Symmetrization results for general nonlocal linear elliptic and parabolic problems

Vincenzo Ferone
Universit\`a di Napoli Federico II
Italy
Co-Author(s):    
Abstract:
We discuss a Talenti-type symmetrization result in the form of mass concentration (\emph{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 previous results obtained in collaboration with B. Volzone. Also a Cauchy-Dirichlet nonlocal linear parabolic problem is considered.