Critical Hardy-Sobolev inequalities

被引：63
|
作者：
Filippas, S. [1 ]
Maz'ya, V.
Terfikas, A.
机构：
[1] Univ Crete, Dept Appl Math, Iraklion 71409, Greece
[2] FORTH, Inst Appl & Computat Math, Iraklion 71110, Greece
[3] Univ Liverpool, Dept Math Sci, Liverpool L69 72L, Merseyside, England
[4] Ohio State Univ, Dept Math, Columbus, OH 43210 USA
[5] Univ Crete, Dept Math, Iraklion 71409, Greece
来源：
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2007年 / 87卷 / 01期
关键词：
Hardy inequality; Sobolev inequality; distance function; critical exponent; convexity; isoperimetric inequality;
D O I：
10.1016/j.matpur.2006.10.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider Hardy inequalities in R-n, n >= 3, with best constant that involve either distance to the boundary or distance to a surface of co-dimension k < n, and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm. (C) 2006 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：37 / 56
页数：20
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