On the classical solvability of near field reflector problems

Jiakun  Liu; Neil S. Trudinger

doi:10.3934/dcds.2016.36.895

Article Contents

2016, Volume 36, Issue 2: 895-916. Doi: 10.3934/dcds.2016.36.895

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On the classical solvability of near field reflector problems

Jiakun Liu^1, and
Neil S. Trudinger^2,

1.
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522
2.
Centre for Mathematics and Its Applications, the Australian National University, Canberra, ACT 0200

Received: June 30, 2014

Revised: February 28, 2015

Published: May 2017

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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 parallel light source, with planar receivers. These problems involve Monge-Ampère 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 conditions by Li, Liu and Nguyen.

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Mathematics Subject Classification: Primary: 35J60; Secondary: 78A05.

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