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.

arXiv comment44 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 (10)

• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure
• Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in RCD(K,\infty) metric measure spaces
• Energy measures and indices of Dirichlet forms, with applications to derivatives on some fractals
• Modified Massive Arratia flow and Wasserstein diffusion
• The Dirichlet-Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold
• A Rademacher-type Theorem on $L^2$-Wasserstein Spaces over Closed Riemannian Manifolds
• Configuration spaces over singular spaces -- I. Dirichlet-Form and Metric Measure Geometry

Cited by in corpus (4)

• Sobolev-to-Lipschitz Property on QCD-spaces and Applications
• Curvature bound of Dyson Brownian Motion
• Integral Varadhan formula for non-linear heat flow
• Persistence of Rademacher-type and Sobolev-to-Lipschitz properties