Fractional Sobolev-Hardy inequality in RN

被引：37
作者：
Yang, Jianfu [1 ]
机构：
[1] Jiangxi Normal Univ, Dept Math, Nanchang 330022, Jiangxi, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 119卷
关键词：
Sobolev-Hardy inequality; Minimizer; Radial symmetry; Decaying law; CONSTANTS;
D O I：
10.1016/j.na.2014.09.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we show that the minimizing problem Lambda(s,alpha) = inf(u(H) over dots(RN), u not equivalent to 0) integral(RN)vertical bar-Delta(s/2)u(x)vertical bar(2) dx/(integral(RN)vertical bar u(x)vertical bar(2)*(s,alpha)/vertical bar x vertical bar(alpha) dx)(2/2)*(s,alpha) (1) is achieved by a positive, radially symmetric and strictly decreasing function provided 0 < s < N/2, 0 < alpha < 2s. (C) 2014 Elsevier Ltd. All rights reserved.
引用
收藏
页码：179 / 185
页数：7
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