Comparison results for the solutions to the anisotropic Laplacian with Robin boundary conditions

Abstract

In this paper we consider PDE's problems involving the anisotropic Laplacian operator, with Robin boundary conditions. By means of Talenti techniques, widely used in the last decades, we prove a comparison result between the solutions of the above-mentioned problems and the solutions of the symmetrized ones. As a consequence of these results, a Bossel-Daners type inequality can be shown in dimension 2. MSC 2010: 35B51 -35G20 -35G30 -35J60 -35P15

A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions

“…Recently quite a few papers dealing with a priori estimates and Robin boundary conditions have appeared, some of them (see, for instance, [15,16]) simply inspired by our result, others (as for instance [3,17]) generalize our technique to nonlinear contexts.…”