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On the classical solvability of near field reflector problems

Journal Article


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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 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.

Authors


Publication Date


  • 2016

Citation


  • 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.

Scopus Eid


  • 2-s2.0-84942342565

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5588&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4567

Number Of Pages


  • 21

Start Page


  • 895

End Page


  • 916

Volume


  • 2

Issue


  • 2

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.

Authors


Publication Date


  • 2016

Citation


  • 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.

Scopus Eid


  • 2-s2.0-84942342565

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5588&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4567

Number Of Pages


  • 21

Start Page


  • 895

End Page


  • 916

Volume


  • 2

Issue


  • 2