On Harnack inequalities and optimal transportation
Probability
2013-07-09 v4
Abstract
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 the heat flow contraction property along Wasserstein distances.
Keywords
Cite
@article{arxiv.1210.4650,
title = {On Harnack inequalities and optimal transportation},
author = {Dominique Bakry and Ivan Gentil and Michel Ledoux},
journal= {arXiv preprint arXiv:1210.4650},
year = {2013}
}