On the classical solvability of near field reflector problems

Authors

Jiakun Liu, University of WollongongFollow
Neil Trudinger, Australian National UniversityFollow

RIS ID

102484

Publication Details

Liu, J. & Trudinger, N. (2016). On the classical solvability of near field reflector problems. Discrete and Continuous Dynamical Systems Series A, 2 (2), 895-916.

Abstract

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.