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arXiv · 1703.09385

Elliptic Harnack inequalities for symmetric non-local Dirichlet forms

Zhen-Qing Chen·Takashi Kumagai·Jian Wang
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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.

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Zhen-Qing Chen, Takashi Kumagai, Jian Wang. 2017-09-05. Elliptic Harnack inequalities for symmetric non-local Dirichlet forms. https://arxiv.org/abs/1703.09385

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