The sharp Sobolev inequality in quantitative form

被引：72
作者：
Cianchi, A. [1 ]
Fusco, N. [2 ]
Maggi, F. [3 ]
Pratelli, A. [4 ]
机构：
[1] Dipartimento Matemat & Applicaz Architettura, I-50122 Florence, Italy
[2] Dipartimento Matemat & Applicaz, I-80126 Naples, Italy
[3] Dipartimento Matemat, I-50134 Florence, Italy
[4] Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2009年 / 11卷 / 05期
关键词：
ISOPERIMETRIC INEQUALITY; BOUNDED VARIATION; PRINCIPLE; REARRANGEMENTS; ASYMMETRY; DOMAINS;
D O I：
10.4171/JEMS/176
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A quantitative version of the sharp Sobolev inequality in W(1, p)(R(n)), 1 < p < n, is established with a remainder term involving the distance from the family of extremals.
引用
收藏
页码：1105 / 1139
页数：35
相关论文
共 26 条
[21]  
LIONS PL, 1984, ANN I H POINCARE-AN, V1, P109
[22]   Improved Sobolev inequalities on the Heisenberg group [J].
Loiudice, A .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 62 (05) :953-962
[23]  
Lutwak E, 2002, J DIFFER GEOM, V62, P17
[24]   Balls have the worst best Sobolev inequalities [J].
Maggi, F ;
Villani, C .
JOURNAL OF GEOMETRIC ANALYSIS, 2005, 15 (01) :83-121
[25]  
Struwe M., 1996, Ergeb. Math. Grenzgeb., V34
[26]  
Talenti G., 1976, ANN MAT PUR APPL, V110, P353, DOI [DOI 10.1007/BF02418013, 10.1007/bf02418013]
123