Weak solutions of one inverse problem in geometric optics

被引：2
|
作者：
Caffarelli L.A. [1 ]
Oliker V.I. [2 ]
机构：
[1] University of Texas at Austin, 1 University Station, C1200, Austin
[2] Emory University, Atlanta, GA 30322, 400 Dowman Dr.
来源：
Journal of Mathematical Sciences | 2008年 / 154卷 / 1期
基金：
美国国家科学基金会;
关键词：
Weak Solution; Unit Sphere; Convex Body; Radial Function; Geometric Optic;
D O I：
10.1007/s10958-008-9152-x
中图分类号：
学科分类号：
摘要：
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. © 2008 Springer Science+Business Media, Inc.
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页码：39 / 49
页数：10
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