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

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.

24 pages