The two dimensional Lp Minkowski problem and nonlinear equations with negative exponents

被引：42

作者：

Dou, Jingbo ^{[1
,2
]}

Zhu, Meijun ^{[2
]}

机构：

[1] Xian Univ Finance & Econ, Sch Stat, Xian 710100, Shaanxi, Peoples R China

[2] Univ Oklahoma, Dept Math, Norman, OK 73019 USA

来源：

ADVANCES IN MATHEMATICS | 2012年 / 230卷 / 03期

基金：

中国国家自然科学基金;

关键词：

L-p Minkowski problem; Negative exponent; Blaschke-Santalo inequality; ELLIPTIC EQUATION; CLASSIFICATION;

D O I：

10.1016/j.aim.2012.02.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we present various existence results for nonlinear differential equations related to the L-p Minkowski problem in the plane and the one dimensional conformal curvature problem. In particular, the supercritical case (that is p < -2) for the L-p Minkowski problem with sign-changing data is addressed. A new geometric sharp inequality is also obtained. Published by Elsevier Inc.

引用

页码：1209 / 1221

页数：13

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