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.

引用

页码：39 / 49

页数：10

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