On the Lp Monge - Ampere equation

被引：73

作者：

Chen, Shibing ^{[1
]}

Li, Qi-rui ^{[1
]}

Zhu, Guangxian ^{[2
]}

机构：

[1] Australian Natl Univ, Math Sci Inst, Canberra, ACT 2601, Australia

[2] NYU, Tandon Sch Engn, Dept Math, 6 Metrotech, Brooklyn, NY 11201 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 08期

关键词：

Monge Ampere type equation; L-p surface area measure; L-p Minkowski problem; CHRISTOFFEL-MINKOWSKI PROBLEM; SURFACE MEASURE; CLASSIFICATION; REGULARITY; UNIQUENESS; GEOMETRY; SPHERE;

D O I：

10.1016/j.jde.2017.06.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For the case where 0 < p < 1, we prove the existence of solutions of the L-p Monge Ampere equation for arbitrary measures and show that the solution is in general not unique. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：4997 / 5011

页数：15

共 64 条

[1]

Alexandroff A, 1942, CR ACAD SCI URSS, V35, P131

[2]

Andrews B, 2003, J AM MATH SOC, V16, P443

[3] Gauss curvature flow: the fate of the rolling stones [J].

Andrews, B .

INVENTIONES MATHEMATICAE, 1999, 138 (01) :151-161

[4] A probabilistic approach to the geometry of the lnp-ball [J].

Barthe, F ;

Guédon, O ;

Mendelson, S ;

Naor, A .

ANNALS OF PROBABILITY, 2005, 33 (02) :480-513

[5] Cone-volume measure of general centered convex bodies [J].

Boeroeczky, Karoly J. ;

Henk, Martin .

ADVANCES IN MATHEMATICS, 2016, 286 :703-721

[6]

Böröczky KJ, 2013, J AM MATH SOC, V26, P831

[7] The log-Brunn-Minkowski inequality [J].

Boeroeczky, Karoly J. ;

Lutwak, Erwin ;

Yang, Deane ;

Zhang, Gaoyong .

ADVANCES IN MATHEMATICS, 2012, 231 (3-4) :1974-1997

[8]

Boroczky K. J., PLANAR LP MINKOWSKI

[9]

Boroczky K. J., DUAL MINKOWSKI PROBL

[10] On the Discrete Logarithmic Minkowski Problem [J].

Boroczky, Karoly J. ;

Hegedus, Pal ;

Zhu, Guangxian .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016, 2016 (06) :1807-1838

← 1 2 3 4 5 6 7 →