On the classical solvability of near field reflector problems

In this paper we prove the existence of classical solutions to near field reflector problems, both for a point light source and for a parrallel light source, with planar recievers. These problems involve monge-Ampere type equations, subject to nonlinear oblique boundary conditions. Our approach builds on earlier work in the optimal transportation case by Trudinger and Wang and makes use of a recent extension of degree theory to oblique boundary conditioins by Li, Liu and Nguyen.