OBLIQUE BOUNDARY-VALUE-PROBLEMS FOR EQUATIONS OF MONGE-AMPERE TYPE

We prove the existence of classical solutions of elliptic equations of Monge-Ampere type subject to a semilinear oblique boundary condition which is a C-1 perturbation of the Neumann boundary condition. Our tec hniques also allow us to treat fully nonlinear strictly oblique bounda ry conditions satisfying a concavity condition. Examples show that the above restrictions on the boundary condition are generally necessary for the existence of classical solutions.