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

Jean Christophe Mourrat, Felix Otto

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)201-228
Number of pages28
JournalJournal of Functional Analysis
Volume270
Issue number1
DOIs
StatePublished - Jan 1 2016

Keywords

  • Diffusion in dynamic random medium
  • Heat kernel
  • Nash inequality

ASJC Scopus subject areas

  • Analysis

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