CLASSIFICATION OF EXTREMAL FUNCTIONS TO LOGARITHMIC HARDY-LITTLEWOOD-SOBOLEV INEQUALITY ON THE UPPER HALF SPACE

被引：4

作者：

Dou, Jingbo ^{[1
]}

Li, Ye ^{[2
]}

机构：

[1] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710119, Shaanxi, Peoples R China

[2] Cent Michigan Univ, Dept Math, Mt Pleasant, MI 48859 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Logarithmic Hardy-Littlewood-Sobolev inequality; extremal functions; integral system; Kelvin transformation; method of moving spheres; CONFORMALLY INVARIANT EQUATIONS; ELLIPTIC-EQUATIONS; MOSER-TRUDINGER; MOVING SPHERES; THEOREMS; UNIQUENESS;

D O I：

10.3934/dcds.2018171

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we mainly classify the extremal functions of logarithmic Hardy-Littlewood-Sobolev inequality on the upper half space R-+(n), and also present some remarks on the extremal functions of logarithmic Hardy-Littlewood-Sobolev inequality on the whole space R-n. Our main techniques are Kelvin transformation and the method of moving spheres in integral forms.

引用

页码：3939 / 3953

页数：15

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