Hamilton Jacobi equations on metric spaces and transport-entropy inequalities
Probability
2012-03-14 v1 Functional Analysis
Abstract
We prove an Hopf-Lax-Oleinik formula for the solutions of some Hamilton- Jacobi equations on a general metric space. As a first consequence, we show in full gener- ality that the log-Sobolev inequality is equivalent to an hypercontractivity property of the Hamilton-Jacobi semi-group. As a second consequence, we prove that Talagrand's transport- entropy inequalities in metric space are characterized in terms of log-Sobolev inequalities restricted to the class of c-convex functions.
Keywords
Cite
@article{arxiv.1203.2783,
title = {Hamilton Jacobi equations on metric spaces and transport-entropy inequalities},
author = {Nathael Gozlan and Cyril Roberto and Paul-Marie Samson},
journal= {arXiv preprint arXiv:1203.2783},
year = {2012}
}
Comments
27 pages