Faber-Krahn inequality for anisotropic eigenvalue problems with Robin boundary conditions

TL;DR

This paper investigates the properties of the first eigenvalue and eigenfunctions of nonlinear elliptic operators with Robin boundary conditions, establishing a Faber-Krahn inequality for anisotropic cases in Lipschitz domains.

Contribution

It introduces a Faber-Krahn inequality for anisotropic nonlinear elliptic operators with Robin boundary conditions, expanding understanding of eigenvalue problems in this context.

Findings

First eigenvalue properties characterized

Faber-Krahn inequality proved for anisotropic operators

Eigenfunctions analyzed in Lipschitz domains

Abstract

In this paper we study the main properties of the first eigenvalue and its eigenfunctions of a class of highly nonlinear elliptic operators in a bounded Lipschitz domain, assuming a Robin boundary condition. Moreover, we prove a Faber-Krahn inequality.