Rademacher-type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces

Abstract

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.

44 pages, list of notations (end), Title, Abstract and Introduction have been changed. Lemma 2.10, Corollary 2.35, and Proposition 3.31 have been removed. Proposition 3.7 and Corollary 4.17 have been added

References in corpus (1)

• Configuration spaces over singular spaces -- I. Dirichlet-Form and Metric Measure Geometry

Cited by in corpus (4)

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• Persistence of Rademacher-type and Sobolev-to-Lipschitz properties