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

[21] THE CANONICAL EXPANDING SOLITON AND HARNACK INEQUALITIES FOR RICCI FLOW [J].

Cabezas-Rivas, Esther ;

Topping, Peter M. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (06) :3001-3021

[22] New boundary Harnack inequalities with right hand side [J].

Ros-Oton, Xavier ;

Torres-Latorre, Clara .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 288 :204-249

[23] A note on transportation cost inequalities for diffusions with reflections [J].

Pal, Soumik ;

Sarantsev, Andrey .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2019, 24

[24] Transportation-information inequalities for Markov processes [J].

Guillin, Arnaud ;

Leonard, Christian ;

Wu, Liming ;

Yao, Nian .

PROBABILITY THEORY AND RELATED FIELDS, 2009, 144 (3-4) :669-695

[25] Parabolic Boundary Harnack Inequalities with Right-Hand Side [J].

Torres-Latorre, Clara .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2024, 248 (05)

[26] Harnack inequalities for SDEs driven by subordinator fractional Brownian motion [J].

Li, Zhi ;

Yan, Litan .

STATISTICS & PROBABILITY LETTERS, 2018, 134 :45-53

[27] A Note on Harnack Inequalities and Propagation Sets for a Class of Hypoelliptic Operators [J].

Cinti, Chiara ;

Nystrom, Kaj ;

Polidoro, Sergio .

POTENTIAL ANALYSIS, 2010, 33 (04) :341-354

[28] Harnack inequalities and heat kernel estimates for SDEs with singular drifts [J].

Shao, Jinghai .

BULLETIN DES SCIENCES MATHEMATIQUES, 2013, 137 (05) :589-601

[29] Weak Harnack Inequalities for Eigenvalues and the Monotonicity of Hessian's Rank [J].

Xu, Lu ;

Yan, Bianlian .

ANALYSIS IN THEORY AND APPLICATIONS, 2023, 39 (02) :147-162

[30] Harnack inequalities for a class of heat flows with nonlinear reaction terms [J].

Abolarinwa, Abimbola ;

Ehigie, Julius Osato ;

Alkhaldi, Ali H. .

JOURNAL OF GEOMETRY AND PHYSICS, 2021, 170

← 1 2 3 4 5 →