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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2020
- DOI:
- 10.48550/arXiv.2008.01492
- arXiv:
- arXiv:2008.01492
- Bibcode:
- 2020arXiv200801492D
- Keywords:
-
- Mathematics - Functional Analysis;
- Mathematics - Metric Geometry;
- Mathematics - Probability;
- 31C25 (Primary) 30L99;
- 31E05 (Secondary)
- E-Print:
- 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