Critical Hardy-Sobolev inequalities

被引：67

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

页码：37 / 56

页数：20

共 22 条

[1] An improved Hardy-Sobolev inequality in W1,p and its application to Schrodinger operators [J].