Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms
Probability
2020-06-19 v5 Analysis of PDEs
Functional Analysis
Metric Geometry
Abstract
In this paper, we establish stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms on metric measure spaces under general volume doubling condition. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cutoff Sobolev inequalities, and Poincar\'e inequalities. In particular, we establish the connection between parabolic Harnack inequalities and two-sided heat kernel estimates, as well as with the H\"older regularity of parabolic functions for symmetric non-local Dirichlet forms.
Keywords
Cite
@article{arxiv.1609.07594,
title = {Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms},
author = {Zhen-Qing Chen and Takashi Kumagai and Jian Wang},
journal= {arXiv preprint arXiv:1609.07594},
year = {2020}
}
Comments
61 pages, 1 figure; arXiv version