English

Elliptic Harnack inequalities for symmetric non-local Dirichlet forms

Probability 2017-09-06 v2 Analysis of PDEs

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 H\"older 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.

Keywords

Cite

@article{arxiv.1703.09385,
  title  = {Elliptic Harnack inequalities for symmetric non-local Dirichlet forms},
  author = {Zhen-Qing Chen and Takashi Kumagai and Jian Wang},
  journal= {arXiv preprint arXiv:1703.09385},
  year   = {2017}
}

Comments

40 pages

R2 v1 2026-06-22T18:58:49.949Z