Non-uniformly parabolic equations and applications to the random conductance model
Peter Bella, Mathias Schäffner · Probability Theory and Related Fields · 2021
Abstract We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on $$\mathbb Z^d$$ Zd . 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.