Elliptic Harnack inequalities for symmetric non-local Dirichlet forms

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.

40 pages

References in corpus (1)

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

Cited by in corpus (2)

• Parabolic Harnack inequality implies the existence of jump kernel
• Random conductance models with stable-like jumps: heat kernel estimates and Harnack inequalities