On Harnack inequalities and optimal transportation

被引：0

作者：

Bakry, Dominique ^{[1
]}

Gentil, Ivan ^{[1
]}

Ledoux, Michel ^{[2
]}

机构：

[1] Univ Toulouse Paul Sebatier, Inst Math Toulouse, F-31062 Toulouse, France

[2] Univ Lyon 1, Inst Camille Jordan, CNRS UMR 5208, F-69622 Lyon, France

来源：

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE | 2015年 / 14卷 / 03期

关键词：

METRIC-MEASURE-SPACES; CURVATURE-DIMENSION CONDITION; RICCI CURVATURE; WASSERSTEIN DISTANCE; EULERIAN CALCULUS; EQUATIONS; GEOMETRY; HYPERCONTRACTIVITY; CONTRACTION; MANIFOLDS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop connections between Harnack inequalities for the heat flow of diffusion operators with curvature bounded from below and optimal transportation. Through heat kernel inequalities, a new isoperimetric-type Harnack inequality is emphasized. Commutation properties between the heat and Hopf-Lax semigroups are developed consequently, providing direct access to heat flow contraction in Wasserstein spaces

引用

页码：705 / 727

页数：23

共 50 条

[1] Submanifolds, isoperimetric inequalities and optimal transportation
Castillon, Philippe
JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 259 (01) : 79 - 103
[2] Inequalities for generalized entropy and optimal transportation
Cordero-Erausquin, D
Gangbo, W
Houdré, C
RECENT ADVANCES IN THE THEORY AND APPLICATIONS OF MASS TRANSPORT, 2004, 353 : 73 - 94
[3] Nonlocal Harnack inequalities
Di Castro, Agnese
Kuusi, Tuomo
Palatucci, Giampiero
JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 267 (06) : 1807 - 1836
[4] LOGARITHMIC HARNACK INEQUALITIES
Chung, F. R. K.
Yau, S. -T.
MATHEMATICAL RESEARCH LETTERS, 1996, 3 (06) : 793 - 812
[5] Harnack Inequalities: An Introduction
Moritz Kassmann
Boundary Value Problems, 2007
[6] Harnack inequalities: An introduction
Kassmann, Moritz
BOUNDARY VALUE PROBLEMS, 2007, 2007 (1)
[7] Harnack and shift Harnack inequalities for SDEs with integrable drifts
Huang, Xing
STOCHASTICS AND DYNAMICS, 2019, 19 (05)
[8] Stability of elliptic Harnack inequalities
Zhen-Qing Chen
Science China Mathematics, 2023, 66 : 2179 - 2190
[9] Stability of elliptic Harnack inequalities
Chen, Zhen-Qing
SCIENCE CHINA-MATHEMATICS, 2023, 66 (10) : 2179 - 2190
[10] Harnack inequalities for jump processes
Bass, RF
Levin, DA
POTENTIAL ANALYSIS, 2002, 17 (04) : 375 - 388

← 1 2 3 4 5 →