The neumann problem for equations of monge‐ampère type

Abstract

Abstract We prove the existence of a classical solution to a Neumann type problem for nonlinear elliptic equations of Monge‐Ampère type. The methods depend upon the establishment of a priori derivative estimates up to order two and yield a sharp result for the equation of prescribed Gauss curvature. We also present applications to asymptotic problems which approach the non‐unique case and maximum principles for linear equations of Aleksandrov‐Bakelman type.