On the Neumann problem for Monge-Ampère type equations

In this paper, we study the global regularity for regular Monge-Ampere 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-Ampere case by Lions, Trudinger, and Urbas in 1986 and the recent barrier con-structions 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.