A supersolutions perspective on hypercontractivity

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...

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Bibliographic Details
Published inAnnali di matematica pura ed applicata Vol. 199; no. 5; pp. 2105 - 2116
Main Authors Aoki, Yosuke, Bennett, Jonathan, Bez, Neal, Machihara, Shuji, Matsuura, Kosuke, Shiraki, Shobu
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2020
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Hypercontractivity
Supersolutions
Markov semigroup
47D07
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Summary: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.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-020-00958-7