Isoperimetric estimates for solutions to the p-Laplacian with variable Robin boundary conditions

TL;DR

This paper investigates the p-Poisson equation with variable Robin boundary conditions, establishing sharp bounds for solutions using weighted isoperimetric inequalities and deriving a Faber-Krahn-type inequality.

Contribution

It introduces new sharp bounds for solutions to the p-Poisson equation with variable Robin parameters using weighted isoperimetric inequalities and presents a novel Faber-Krahn-type inequality.

Findings

Derived sharp bounds for solutions to the p-Poisson equation with variable Robin conditions.

Established a Faber-Krahn-type inequality for the problem.

Extended isoperimetric inequalities to weighted settings for these PDEs.

Abstract

In this paper we study the $p$-Poisson equation with Robin boundary conditions, where the Robin parameter is a function. By means of some weighted isoperimetric inequalities, we provide various sharp bounds for the solutions to the problems under consideration. We also derive a Faber-Krahn-type inequality.