Quantitative analysis of some system of integral equations

被引：96

作者：

Jin, Chao ^{[1
]}

Li, Congming ^{[1
]}

机构：

[1] Univ Colorado, Dept Math Appl, Boulder, CO 80309 USA

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2006年 / 26卷 / 04期

关键词：

weighted Hardy-Littlewood-Sobolev inequalities; integral equations and systems; radial symmetry; monotonicity; moving planes in integral forms;

D O I：

10.1007/s00526-006-0013-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the integrability of the non-negative solutions to the Euler-Lagrange equations associated with Weighted Hardy-Littlewood-Sobolev (HLS) inequality. We obtain the optimal integrability for the solutions. The integrability and the radial symmetry (which we derived in our earlier paper) are the key ingredients to study the growth rate at the center and the decay rate at infinity of the solutions. These are also the essential properties needed to classify all non-negative solutions. Some simple generalizations are also provided here.

引用

页码：447 / 457

页数：11

共 24 条

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[Anonymous], 2000, CAMBRIDGE TRACTS MAT

[2] SHARP SOBOLEV INEQUALITIES ON THE SPHERE AND THE MOSER-TRUDINGER INEQUALITY [J].