Principal eigenvalues for Isaacs operators with Neumann boundary conditions

TL;DR

This paper establishes the existence and properties of principal eigenvalues for non-convex fully nonlinear elliptic operators with Neumann boundary conditions, and discusses related regularity, uniqueness, and existence results.

Contribution

It introduces the concept of two principal eigenvalues for non-convex operators with Neumann conditions and analyzes their fundamental properties.

Findings

Existence of two principal eigenvalues for the operators.

Basic properties of these eigenvalues are established.

Lipschitz regularity, uniqueness, and existence results for the Neumann problem.

Abstract

In this paper we show the existence of two principal eigenvalues associated to general non-convex fully nonlinear elliptic operators with Neumann boundary conditions in a bounded $C^2$ domain. We study these objects and we establish some of their basic properties. Finally, Lipschitz regularity, uniqueness and existence results for the solution of the Neumann problem are given.