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

共 50 条

[1] On a Priori Estimates of Weak Solutions of one Nongomogeneous Problem of Dynamics of Viscoelastic Medium with Memory
V. G. Zvyagin
V. P. Orlov
Russian Mathematics, 2021, 65 : 30 - 39
[2] On a Priori Estimates of Weak Solutions of one Nongomogeneous Problem of Dynamics of Viscoelastic Medium with Memory
Zvyagin, V. G.
Orlov, V. P.
RUSSIAN MATHEMATICS, 2021, 65 (05) : 30 - 39
[3] REGULARITY OF WEAK SOLUTIONS TO A CLASS OF NONLINEAR PROBLEM
周建丰
谭忠
Acta Mathematica Scientia, 2021, 41 (04) : 1333 - 1365
[4] Regularity of Weak Solutions to a Class of Nonlinear Problem
Zhou, Jianfeng
Tan, Zhong
ACTA MATHEMATICA SCIENTIA, 2021, 41 (04) : 1333 - 1365
[5] Regularity of Weak Solutions to a Class of Nonlinear Problem
Jianfeng Zhou
Zhong Tan
Acta Mathematica Scientia, 2021, 41 : 1333 - 1365
[6] TRIPLE WEAK SOLUTIONS FOR A KIRCHHOFF-TYPE PROBLEM
Tavani, Mohammad reza heidari
Nazari, Abdollah
TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE, 2024, 178 (03) : 503 - 514
[7] Weak Solutions for a Second Order Impulsive Boundary Value Problem
Zhang, Keyu
Xu, Jiafa
O'Regan, Donal
FILOMAT, 2017, 31 (20) : 6431 - 6439
[8] The existence of the weak solutions of the three-dimensional infiltration problem
Fang Ping
Zhou Yu-Zhong
Song Rui-Feng
Zhang Xin
2009 INTERNATIONAL SYMPOSIUM ON WEB INFORMATION SYSTEMS AND APPLICATIONS, PROCEEDINGS, 2009, : 339 - 342
[9] Weak solutions of the Cauchy problem in the set of radon probability measures
Kuzenkov, OA
DIFFERENTIAL EQUATIONS, 2000, 36 (11) : 1676 - 1684
[10] The uniqueness of the weak solutions of the three-dimensional infiltration problem
Fang Ping
Zhou Yu-Zhong
Zhang Xin
Song Rui-Feng
IITAW: 2009 THIRD INTERNATIONAL SYMPOSIUM ON INTELLIGENT INFORMATION TECHNOLOGY APPLICATIONS WORKSHOPS, 2009, : 14 - 16

← 1 2 3 4 5 →