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Journal Articles Journal of Functional Analysis Year : 2016

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

Abstract

We introduce anchored versions of the Nash inequality. They allow to control the L 2 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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Dates and versions

ensl-01401897 , version 1 (23-11-2016)

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Jean-Christophe Mourrat, Felix Otto. Anchored Nash inequalities and heat kernel bounds for static and dynamic degenerate environments. Journal of Functional Analysis, 2016, 270, pp.201 - 228. ⟨10.1016/j.jfa.2015.09.020⟩. ⟨ensl-01401897⟩
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