On the reflector shape design

Aram Karakhanyan, Xi-Jia Wang

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.
Original languageEnglish
Pages (from-to)561-610
JournalJournal of Differential Geometry
Issue number3
Publication statusPublished - 2010


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