Anchored Nash inequalities and heat kernel bounds for static and dynamic degenerate environments

Jean Christophe Mourrat; Felix Otto

doi:10.1016/j.jfa.2015.09.020

Anchored Nash inequalities and heat kernel bounds for static and dynamic degenerate environments

Jean Christophe Mourrat, Felix Otto

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce anchored versions of the Nash inequality. They allow to control the L² norm of a function by Dirichlet forms that are not uniformly elliptic. We then use them to provide heat kernel upper bounds for diffusions in degenerate static and dynamic random environments. As an example, we apply our results to the case of a random walk with degenerate jump rates that depend on an underlying exclusion process at equilibrium.

Original language	English (US)
Pages (from-to)	201-228
Number of pages	28
Journal	Journal of Functional Analysis
Volume	270
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2015.09.020
State	Published - Jan 1 2016

Keywords

Diffusion in dynamic random medium
Heat kernel
Nash inequality

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2015.09.020

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abstract = "We introduce anchored versions of the Nash inequality. They allow to control the L2 norm of a function by Dirichlet forms that are not uniformly elliptic. We then use them to provide heat kernel upper bounds for diffusions in degenerate static and dynamic random environments. As an example, we apply our results to the case of a random walk with degenerate jump rates that depend on an underlying exclusion process at equilibrium.",

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AB - We introduce anchored versions of the Nash inequality. They allow to control the L2 norm of a function by Dirichlet forms that are not uniformly elliptic. We then use them to provide heat kernel upper bounds for diffusions in degenerate static and dynamic random environments. As an example, we apply our results to the case of a random walk with degenerate jump rates that depend on an underlying exclusion process at equilibrium.

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Anchored Nash inequalities and heat kernel bounds for static and dynamic degenerate environments

Abstract

Keywords

ASJC Scopus subject areas

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