A supersolutions perspective on hypercontractivity
Functional Analysis
2019-05-21 v1 Analysis of PDEs
Probability
Abstract
The purpose of this article is to expose an algebraic closure property of supersolutions to certain diffusion equations. This closure property quickly gives rise to a monotone quantity which generates a hypercontractivity inequality. Our abstract argument applies to a general Markov semigroup whose generator is a diffusion and satisfies a curvature condition.
Cite
@article{arxiv.1905.07911,
title = {A supersolutions perspective on hypercontractivity},
author = {Yosuke Aoki and Jonathan Bennett and Neal Bez and Shuji Machihara and Kosuke Matsuura and Shobu Shiraki},
journal= {arXiv preprint arXiv:1905.07911},
year = {2019}
}
Comments
7 pages