Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces

摘要

We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms. (C) 2021 Elsevier Inc. All rights reserved.