On the viscosity solutions to some nonlinear elliptic equations

Abstract

We consider viscosity solutions of a class of nonlinear degenerate elliptic equations on bounded domains. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many instances, show the existence of a first eigenvalue and a first positive eigenfunction.

33 pages. The work underwent a significant revision. The work has been expanded and generalized, relevant examples included and important references added