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Weak solutions of one inverse problem in geometric optics

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Abstract

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.

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Authors and Affiliations

  1. University of Texas at Austin, 1 University Station, C1200, Austin, Texas, 78712-1082, USA

    L. A. Caffarelli

  2. Emory University, 400 Dowman Dr., W401, Atlanta, GA, 30322, USA

    V. I. Oliker

Authors
  1. L. A. Caffarelli
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  2. V. I. Oliker
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Correspondence to L. A. Caffarelli.

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__________

Translated from Problemy Matematicheskogo Analiza, No. 37, 2008, pp. 37–46.

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Caffarelli, L.A., Oliker, V.I. Weak solutions of one inverse problem in geometric optics. J Math Sci 154, 39–49 (2008). https://doi.org/10.1007/s10958-008-9152-x

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  • DOI: https://doi.org/10.1007/s10958-008-9152-x

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