Non-uniformly parabolic equations and applications to the random conductance model

Peter Bella; Mathias Schäffner

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arXiv · 2009.11535

Non-uniformly parabolic equations and applications to the random conductance model

Peter Bella·Mathias Schäffner

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Abstract

We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on $\mathbb Z^d$. In particular, we provide an oscillation decay assuming only certain summability properties of the conductances and their inverse, thus improving recent results in that direction. As an application, we provide a local limit theorem for the random walk in a random degenerate and unbounded environment.

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Peter Bella, Mathias Schäffner. 2020-09-24. Non-uniformly parabolic equations and applications to the random conductance model. https://arxiv.org/abs/2009.11535

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