Boundary regularity for the Monge–Ampère and affine maximal surface equations

Abstract

In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the Monge-Ampère equation when the inhomogeneous term is only assumed to be Hölder continuous. As a consequence of our approach, we also establish the existence and uniqueness of globally smooth solutions to the second boundary value problem for the affine maximal surface equation and affine mean curvature equation.

Authors

Neil S. Trudinger

Mathematical Sciences Institute
The Australian National University
Canberra 0200
Australia

Xu-Jia Wang

Mathematical Sciences Institute
The Australian National University
Canberra 0200
Australia