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

By Zhen-Qing Chen, Takashi Kumagai, Jian Wang. 2016

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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 Poincare inequalities. In particular, we establish the connection between parabolic Harnack inequalities and two-sided heat kernel estimates, as well as with the Holder regularity of parabolic functions for symmetric non-local Dirichlet forms.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/8019898a50604b2ce1a315316f55396fcfc36ef2