On the Dirichlet problem for general augmented Hessian equations

Abstract

In this paper we apply various first and second derivative estimates and barrier constructions from our treatment of oblique boundary value problems for augmented Hessian equations, to the case of Dirichlet boundary conditions. As a result we extend our previous results on the Monge-Ampere and k-Hessian cases to general classes of augmented Hessian equations in Euclidean space

This paper is a spin-off from our treatment of oblique boundary value problems which was first posted on arXiv in 2015 and replaces earlier drafts