Hamilton-Jacobi Equations on Graph and Applications

被引：9

作者：

Shu, Yan ^{[1
]}

机构：

[1] Modelisat Aleatoire Paris Ouest Nanterre La Def M, Nanterre, France

来源：

POTENTIAL ANALYSIS | 2018年 / 48卷 / 02期

关键词：

Hamilton-Jacobi equations; Weak-transport entropy inequalities; Modified Log-Sob inequalities on graphs; LOGARITHMIC SOBOLEV INEQUALITIES; MARKOV-CHAINS; SPACES; TRANSPORT; ENTROPY;

D O I：

10.1007/s11118-017-9628-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper introduces a notion of gradient and an infimal-convolution operator that extend properties of solutions of Hamilton Jacobi equations to more general spaces, in particular to graphs. As a main application, the hypercontractivity of this class of infimal-convolution operators is connected to some discrete version of the log-Sobolev inequality and to a discrete version of Talagrand's transport inequality.

引用

页码：125 / 157

页数：33

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