Existence and Regularity of the Reflector Surfaces in Rn+1

Aram L. Karakhanyan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

In this paper we study the problem of constructing reflector surfaces from the near field data. The light is transmitted as a collinear beam and the reflected rays illuminate a given domain on the fixed receiver surface. We consider two types of weak solutions and prove their equivalence under some convexity assumptions on the target domain. The regularity of weak solutions is a very delicate problem and the positive answer depends on a number of conditions characterizing the geometric positioning of the reflector and receiver. In fact, we show that there is a domain in the ambient space such that the weak solution is smooth if and only if its graph lies in D.

Original languageEnglish
Pages (from-to)833-885
Number of pages53
JournalArchive for Rational Mechanics and Analysis
Volume213
Issue number3
DOIs
Publication statusPublished - Sept 2014

Keywords / Materials (for Non-textual outputs)

  • MONGE-AMPERE EQUATION
  • DESIGN

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