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

TL;DR

This paper establishes comparison results for solutions to anisotropic Laplacian PDEs with Robin boundary conditions using Talenti techniques, leading to inequalities in two dimensions that relate solutions of original and symmetrized problems.

Contribution

It introduces a comparison framework for anisotropic Laplacian problems with Robin boundary conditions using Talenti techniques, and derives a Bossel-Daners type inequality in 2D.

Findings

Comparison results between original and symmetrized solutions

A Bossel-Daners type inequality in dimension 2

Application of Talenti techniques to anisotropic PDEs

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.