Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces

被引：22

作者：

Ambrosio, Luigi ^{[1
]}

Erbar, Matthias ^{[2
]}

Savare, Giuseppe ^{[3
]}

机构：

[1] Scuola Normale Super Pisa, Pisa, Italy

[2] Univ Bonn, Bonn, Germany

[3] Univ Pavia, I-27100 Pavia, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 137卷

基金：

欧洲研究理事会;

关键词：

Optimal transport; Evolution variational inequality; Heat flow; METRIC MEASURE-SPACES; RADEMACHERS THEOREM; DIRICHLET FORMS; GEOMETRY; FLOWS;

D O I：

10.1016/j.na.2015.12.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the setting of extended metric-topological measure spaces as a general "Wiener like" framework for optimal transport problems and nonsmooth metric analysis in infinite dimension. After a brief review of optimal transport tools for general Radon measures, we discuss the notions of the Cheeger energy, of the Radon measures concentrated on absolutely continuous curves, and of the induced "dynamic transport distances". We study their main properties and their links with the theory of Dirichlet forms and the Bakry-Emery curvature condition, in particular concerning the contractivity properties and the EVI formulation of the induced Heat semigroup. (c) 2015 Elsevier Ltd. All rights reserved.

引用

页码：77 / 134

页数：58

共 47 条

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