Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms

Zhen Qing Chen, Takashi Kumagai, Jian Wang

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In this paper, we establish stability of parabolic Harnack inequalities for symmetric nonlocal Dirichlet forms on metric measure spaces under a general volume doubling condition. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cutoff Sobolev inequalities, and Poincaré inequalities. In particular, we establish the connection between parabolic Harnack inequalities and two-sided heat kernel estimates, as well as with the Hölder regularity of parabolic functions for symmetric non-local Dirichlet forms.

Original languageEnglish
Pages (from-to)3747-3803
Number of pages57
JournalJournal of the European Mathematical Society
Volume22
Issue number11
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Hölder regularity
  • Non-local Dirichlet form
  • Parabolic Harnack inequality
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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