Journal of Mathematical Sciences

, Volume 154, Issue 1, pp 39–49 | Cite as

Weak solutions of one inverse problem in geometric optics

  • L. A. CaffarelliEmail author
  • V. I. Oliker


We consider the problem of recovering a closed convex reflecting surface such that for a given point source of light (inside the convex body bounded by the surface) the reflected directions cover a unit sphere with prespecified in advance density. In analytic formulation, the problem leads to an equation of Monge-Ampère type on a unit sphere. We formulate the problem in terms of certain associated measures and establish the existence of weak solutions. Bibliography: 11 titles.


Weak Solution Unit Sphere Convex Body Radial Function Geometric Optic 
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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.University of Texas at AustinAustinUSA
  2. 2.Emory UniversityAtlantaUSA

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