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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.

Keywords

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}
}

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7 pages