Elliptic Harnack inequalities for symmetric non-local Dirichlet forms

Zhen Qing Chen, Takashi Kumagai, Jian Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We study relations and characterizations of various elliptic Harnack inequalities for symmetric non-local Dirichlet forms on metric measure spaces. We allow the scaling function be state-dependent and the state space possibly disconnected. Stability of elliptic Harnack inequalities is established under certain regularity conditions and implication for a priori Hölder regularity of harmonic functions is explored. New equivalent statements for parabolic Harnack inequalities of non-local Dirichlet forms are obtained in terms of elliptic Harnack inequalities.

Original languageEnglish
Pages (from-to)1-42
Number of pages42
JournalJournal des Mathematiques Pures et Appliquees
Volume125
DOIs
Publication statusPublished - 2019 May
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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