Hamilton-Jacobi equations on graph and applications
Functional Analysis
2015-12-09 v1 Probability
Abstract
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.
Cite
@article{arxiv.1512.02416,
title = {Hamilton-Jacobi equations on graph and applications},
author = {Yan Shu},
journal= {arXiv preprint arXiv:1512.02416},
year = {2015}
}
Comments
34 pages, comments are welcome