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arXiv · 1509.01949

Generating monotone quantities for the heat equation

Jonathan Bennett·Neal Bez
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Abstract

The purpose of this article is to expose and further develop a simple yet surprisingly far-reaching framework for generating monotone quantities for positive solutions to linear heat equations in euclidean space. This framework is intimately connected to the existence of a rich variety of algebraic closure properties of families of sub/super-solutions, and more generally solutions of systems of differential inequalities capturing log-convexity properties such as the Li--Yau gradient estimate. Various applications are discussed, including connections with the general Brascamp--Lieb inequality and the Ornstein--Uhlenbeck semigroup.

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Jonathan Bennett, Neal Bez. 2017-05-18. Generating monotone quantities for the heat equation. https://arxiv.org/abs/1509.01949

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