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.
|Journal||Annali di Matematica Pura ed Applicata|
|Publication status||Published - 18 Feb 2020|
Bibliographical note7 pages