Hardy-Poincare inequalities and applications to nonlinear diffusions

被引：42

作者：

Blanchet, Adrien

Bonforte, Matteo

Dolbeault, Jean

Grillo, Gabriele

Vazquez, Juan-Luis

机构：

[1] Univ Paris 09, CEREMADE, F-75775 Paris 16, France

[2] Politecn Torino, Dipartimento Matemat, I-10129 Turin, Italy

[3] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

来源：

COMPTES RENDUS MATHEMATIQUE | 2007年 / 344卷 / 07期

关键词：

D O I：

10.1016/j.crma.2007.01.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We systematically study weighted Poincare type inequalities which are closely connected with Hardy type inequalities and establish the form of the optimal constants in some cases. Such inequalities are then used to relate entropy with entropy production and get intermediate asymptotics results for fast diffusion equations.

引用

页码：431 / 436

页数：6

共 15 条

[1] [Anonymous], 2006, OXFORD LECT SERIES M
[2] BLANCHET A, UNPUB ASYMPTOTICS FA
[3] Global positivity estimates and Harnack inequalities for the fast diffusion equation
Bonforte, Matteo
Vazquez, Juan Luis
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 240 (02) : 399 - 428
[4] Fine asymptotics for fast diffusion equations
Carrillo, JA
Vázquez, JL
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2003, 28 (5-6) : 1023 - 1056
[5] Poincare inequalities for linearizations of very fast diffusion equations
Carrillo, JA
Lederman, C
Markowich, PA
Toscani, G
[J]. NONLINEARITY, 2002, 15 (03) : 565 - 580
[6] Sobolev-Orlicz imbeddings, weak compactness, and spectrum
Cipriani, F
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 177 (01) : 89 - 106
[7] DASKALOPOULOS P, 2006, EXTINCTION PROFILE S
[8] DAVIES E. B, 1999, Oper. Theory Adv. Appl., V110, P55
[9] Davies EB, 1998, MATH Z, V227, P511, DOI 10.1007/PL00004389
[10] Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions
Del Pino, M
Dolbeault, J
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2002, 81 (09): : 847 - 875

← 1 2 →