The principal eigenvalue of the $\infty$-Laplacian with the Neumann boundary condition

TL;DR

This paper establishes the existence of a principal eigenvalue for the infinity-Laplacian with Neumann boundary conditions, providing key results on uniqueness, existence, and decay estimates for related problems.

Contribution

It introduces the first proof of a principal eigenvalue for the infinity-Laplacian with Neumann boundary conditions and derives related existence and decay results.

Findings

Existence of a principal eigenvalue for the infinity-Laplacian with Neumann boundary conditions.

Uniqueness and existence results for the Neumann problem.

Decay estimates for viscosity solutions of the Neumann evolution problem.

Abstract

We prove the existence of a principal eigenvalue associated to the $\infty$-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the Neumann problem and a decay estimate for viscosity solutions of the Neumann evolution problem.