A Neumann eigenvalue problem for fully nonlinear operators

TL;DR

This paper investigates the asymptotic behavior of principal eigenvalues for the Pucci operator with Neumann/Robin boundary conditions, emphasizing boundary Lipschitz estimates and their implications.

Contribution

It provides new insights into the asymptotics of eigenvalues for fully nonlinear operators under boundary conditions, including boundary Lipschitz estimates.

Findings

Asymptotic behavior of eigenvalues as boundary parameter tends to infinity

Development of boundary Lipschitz estimates for fully nonlinear operators

Enhanced understanding of boundary effects on eigenvalues

Abstract

In this paper we study the asymptotic behavior of the principal eigenvalues associated to the Pucci operator in bounded domain $\Omega$ with Neumann/Robin boundary condition i.e. $\partial_n u=\alpha u$ when $\alpha$ tends to infinity. This study requires Lipschitz estimates up to the boundary that are interesting in their own rights.