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Generating Monotone Quantities for the Heat Equation by Bennett, Jonathan; Bez, Neal is a scholarly article available to read on EtoBox.

What is Generating Monotone Quantities for the Heat Equation about?

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.

Author

Bennett, Jonathan; Bez, Neal

Published

2015

Language

EN