Multiple solutions of the Lp-Minkowski problem

被引：0

作者：

He, Yan ^{[1
]}

Li, Qi-Rui ^{[2
]}

Wang, Xu-Jia ^{[2
]}

机构：

[1] Cent S Univ, Sch Math, Changsha 410075, Hunan, Peoples R China

[2] Australian Natl Univ, Ctr Math & Its Applicat, GPO Box 4, Canberra, ACT 2601, Australia

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2016年 / 55卷 / 05期

基金：

澳大利亚研究理事会;

关键词：

ANISOTROPIC CURVATURE FLOW; SIMILAR SHRINKING CURVES; NONUNIQUENESS; INEQUALITIES; EQUATIONS;

D O I：

10.1007/s00526-016-1063-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the existence of multiple solutions to the L-p-Minkowski problem. We prove if p < -n, then for any integer N > 0, there exists a smooth positive function f on S-n such that the L-p-Minkowski problem admits at least N different smooth solutions. We also construct nonsmooth, positive function f for which the L-p-Minkowski problem has infinitely many C-1,C-1 solutions.

引用

页数：13

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