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On the classical solvability of near field reflector problems

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


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