A supersolutions perspective on hypercontractivity

Yosuke Aoki; Jonathan Bennett; Neal Bez; Shuji Machihara; Kosuke Matsuura; Shobu Shiraki

A supersolutions perspective on hypercontractivity

Yosuke Aoki, Jonathan Bennett, Neal Bez, Shuji Machihara, Kosuke Matsuura, Shobu Shiraki

Mathematics

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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.

Original language	English
Journal	Annali di Matematica Pura ed Applicata
Volume	199
Publication status	Published - 18 Feb 2020

Bibliographical note

7 pages

Keywords

math.FA
math.AP
math.PR

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1905.07911v1

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title = "A supersolutions perspective on hypercontractivity",

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. ",

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AU - Aoki, Yosuke

AU - Bennett, Jonathan

AU - Bez, Neal

AU - Machihara, Shuji

AU - Matsuura, Kosuke

AU - Shiraki, Shobu

N1 - 7 pages

PY - 2020/2/18

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AB - 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.

KW - math.FA

KW - math.AP

KW - math.PR

M3 - Article

SN - 0373-3114

VL - 199

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

ER -

A supersolutions perspective on hypercontractivity

Abstract

Bibliographical note

Keywords

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Cite this