Eigenvalue and Dirichlet problem for fully-nonlinear operators in non smooth domains

TL;DR

This paper investigates eigenvalues, maximum principles, and Dirichlet problems for fully nonlinear elliptic operators with singularities or degeneracies in non-smooth domains satisfying the exterior cone condition.

Contribution

It extends the analysis of fully nonlinear elliptic operators to non-smooth domains with singularities, providing new existence and eigenvalue results.

Findings

Established maximum principles for these operators.

Proved existence of eigenvalues and solutions in non-smooth domains.

Extended classical results to more general domain geometries.

Abstract

In this paper we study the maximum principle, the existence of eigenvalue and the existence of solution for the Dirichlet problem for operators which are fully-nonlinear, elliptic but presenting some singularity or degeneracy which are similar to those of the p-Laplacian, the novelty resides in the fact that we consider the equations in bounded domains which only satisfy the exterior cone condition.