Weak solutions of one inverse problem in geometric optics
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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.
KeywordsWeak Solution Unit Sphere Convex Body Radial Function Geometric Optic
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- 1.L. A. Caffarelli and V. I. Oliker, Weak Solutions of One Inverse Problem in Geometric Optics. Preprint, 1994.Google Scholar
- 2.A. D. Aleksandrov, “On the theory of mixed volumes, I: Extension of certain concepts in the theory of convex bodies” [in Russian], Mat. Sb. 2(44) (1937), no. 5, 947–972.Google Scholar
- 11.S. T. Yau, “Open problems in geometry,” in: Proc. Symposia in Pure Mathematics, R. Greene and S. T. Yau, Eds. 54, Part 1, Am. Math. Soc., 1993, pp. 1–28.Google Scholar