From brunn-minkowski to sharp sobolev inequalities

被引：28
作者：
Bobkov, S. G. [1 ]
Ledoux, M. [2 ]
机构：
[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA
[2] Univ Toulouse 3, Inst Math, F-31062 Toulouse, France
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2008年 / 187卷 / 03期
基金：
美国国家科学基金会;
关键词：
46-XX;
D O I：
10.1007/s10231-007-0047-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a simple direct proof of the classical Sobolev inequality in R-n with best constant from the geometric Brunn-Minkowski-Lusternik inequality.
引用
收藏
页码：369 / 384
页数：16
相关论文
共 45 条
[1]  
Adams A, 2003, SOBOLEV SPACES
[2]   Geometric inequalities via a general comparison principle for interacting gases [J].
Agueh, M ;
Ghoussoub, N ;
Kang, X .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2004, 14 (01) :215-244
[3]   Convex symmetrization and applications [J].
Alvino, A ;
Ferone, V ;
Trombetti, G ;
Lions, PL .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (02) :275-293
[4]  
[Anonymous], LECT NOTES MATH
[5]  
[Anonymous], 1993, Encyclopedia of Mathematics and its Applications
[6]  
[Anonymous], 1997, GRADUATE STUDIES MAT
[7]  
Aubin T., 1976, J. Di ff erential Geom., V11, P573
[8]  
Barles G., 1994, Solutions de viscosite des equations de Hamilton-Jacobi, V17
[9]  
Barthe F., 2003, Ann. Fac. Sci. Toulouse Math, V12, P127, DOI DOI 10.5802/AFST.1046
[10]   From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities [J].
Bobkov, SG ;
Ledoux, M .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2000, 10 (05) :1028-1052
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