Open Access
March 2010 On the reflector shape design
Aram Karakhanyan, Xu-Jia Wang
J. Differential Geom. 84(3): 561-610 (March 2010). DOI: 10.4310/jdg/1279114301


In this paper we study the problem of recovering the reflecting surface in a reflector system which consists of a point light source, a reflecting surface, and an object to be illuminated. This problem involves a fully nonlinear partial differential equation of Monge- Ampère type, subject to a nonlinear second boundary condition. A weak solution can be obtained by approximation by piecewise ellipsoidal surfaces. The regularity is a very complicated issue but we found precise conditions for it.


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Aram Karakhanyan. Xu-Jia Wang. "On the reflector shape design." J. Differential Geom. 84 (3) 561 - 610, March 2010.


Published: March 2010
First available in Project Euclid: 14 July 2010

zbMATH: 1201.53007
MathSciNet: MR2669365
Digital Object Identifier: 10.4310/jdg/1279114301

Rights: Copyright © 2010 Lehigh University

Vol.84 • No. 3 • March 2010
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