Generating monotone quantities for the heat equation
-
Jonathan Bennett
and
Neal Bez
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.
To Michael Cowling on his 65th birthday
Funding source: H2020 European Research Council
Award Identifier / Grant number: 307617
Funding statement: The work of the first author was supported by the European Research Council (grant number 307617). The work of the second author was supported by JSPS Kakenhi (grant numbers 26887008 and 16H05995).
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- 𝔸-curves on log smooth varieties
- Generating monotone quantities for the heat equation
- On the global Gan–Gross–Prasad conjecture for unitary groups: Approximating smooth transfer of Jacquet–Rallis
- Poisson manifolds of compact types (PMCT 1)
- A groupoid approach to pseudodifferential calculi
- Duality and socle generators for residual intersections
-
Lower semicontinuity of mass under
- Gravitational instantons with faster than quadratic curvature decay (II)
- Normal subgroups of invertibles and of unitaries in a C*-algebra
Articles in the same Issue
- Frontmatter
- 𝔸-curves on log smooth varieties
- Generating monotone quantities for the heat equation
- On the global Gan–Gross–Prasad conjecture for unitary groups: Approximating smooth transfer of Jacquet–Rallis
- Poisson manifolds of compact types (PMCT 1)
- A groupoid approach to pseudodifferential calculi
- Duality and socle generators for residual intersections
-
Lower semicontinuity of mass under
- Gravitational instantons with faster than quadratic curvature decay (II)
- Normal subgroups of invertibles and of unitaries in a C*-algebra
