On the Neumann problem for Monge-Ampère type equations

Abstract

In this paper, we study the global regularity for regular Monge-Ampère type equations associated with semilinear Neumann boundary conditions. By establishing a priori estimates for second order derivatives, the classical solvability of the Neumann boundary value problem is proved under natural conditions. The techniques build upon the delicate and intricate treatment of the standard Monge-Ampère case by Lions, Trudinger and Urbas in 1986 and the recent barrier constructions and second derivative bounds by Jiang, Trudinger and Yang for the Dirichlet problem. We also consider more general oblique boundary value problems in the strictly regular case.

This version includes some additions and corrections. We are particularly grateful to a referee for careful reading and useful advice

Cited by in corpus (3)

• A degree theory for second order nonlinear elliptic operators with nonlinear oblique boundary conditions
• Monge-Ampère type equations with Neumann boundary conditions on Riemannian manifolds
• Boundary $C^{2,\alpha }$ Regularity for the Oblique Boundary Value Problem of Monge-Ampère Equations