Regularity for the near field parallel refractor and reflector problems

被引：14

作者：

Gutierrez, Cristian E. ^{[1
]}

Tournier, Federico ^{[2
]}

机构：

[1] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

[2] Consejo Nacl Invest Cient & Tecn, Inst Argentino Matemat AP Calderon, RA-1083 Buenos Aires, DF, Argentina

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 54卷 / 01期

基金：

美国国家科学基金会;

关键词：

SURFACES;

D O I：

10.1007/s00526-014-0811-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove local C-1,C-alpha estimates of solutions to the parallel refractor and reflector problems under local assumptions on the target set Sigma, and no assumptions are made on the smoothness of the densities.

引用

页码：917 / 949

页数：33

共 12 条

[1]

[Anonymous], 1990, CLASSICS APPL MATH

[2]

Caffarelli L.A., 2008, J MATH SCI, V154, P37

[3]

Gutierrez C.E., 2013, DEV MATH, V28, P325

[4] The near field refractor [J].

Gutierrez, Cristian E. ;

Huang, Qingbo .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (04) :655-684

[5] The Refractor Problem in Reshaping Light Beams [J].

Gutierrez, Cristian E. ;

Huang, Qingbo .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2009, 193 (02) :423-443

[6]

Karakhanyan A, 2010, J DIFFER GEOM, V84, P561

[7]

Karakhanyan AL, 2014, ARCH RATION MECH AN, V213, P833, DOI 10.1007/s00205-014-0743-z

[8] Determination of reflector surfaces from near-field scattering data [J].

Kochengin, SA ;

Oliker, VI .

INVERSE PROBLEMS, 1997, 13 (02) :363-373

[9] Regularity of Optimal Maps on the Sphere: the Quadratic Cost and the Reflector Antenna [J].

Loeper, Gregoire .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 199 (01) :269-289

[10] On the regularity of solutions of optimal transportation problems [J].

Loeper, Gregoire .

ACTA MATHEMATICA, 2009, 202 (02) :241-283

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