On the Lp Monge - Ampere equation

被引：67
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
收藏
页码：4997 / 5011
页数：15
相关论文
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
    Andrews, B
    [J]. INVENTIONES MATHEMATICAE, 1999, 138 (01) : 151 - 161
  • [4] A probabilistic approach to the geometry of the lnp-ball
    Barthe, F
    Guédon, O
    Mendelson, S
    Naor, A
    [J]. ANNALS OF PROBABILITY, 2005, 33 (02) : 480 - 513
  • [5] Cone-volume measure of general centered convex bodies
    Boeroeczky, Karoly J.
    Henk, Martin
    [J]. ADVANCES IN MATHEMATICS, 2016, 286 : 703 - 721
  • [6] Böröczky KJ, 2013, J AM MATH SOC, V26, P831
  • [7] The log-Brunn-Minkowski inequality
    Boeroeczky, Karoly J.
    Lutwak, Erwin
    Yang, Deane
    Zhang, Gaoyong
    [J]. 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
    Boroczky, Karoly J.
    Hegedus, Pal
    Zhu, Guangxian
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016, 2016 (06) : 1807 - 1838
1234567