The weak elliptic Harnack inequality revisited

2022/08/10 by Jiaxin Hu, Hu, Jiaxin, Yu Zhenyu +1 · 2 citations
Mathematics · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2208.05580

Abstract

In this paper we firstly derive the weak elliptic Harnack inequality from the generalized capacity condition, the tail estimate of jump measure and the Poincaré inequality, for any regular Dirichlet form without killing part on a measure metric space, by using the lemma of growth and the John-Nirenberg inequality. We secondly show several equivalent characterizations of the weak elliptic Harnack inequality for any (not necessarily regular) Dirichlet form. We thirdly present some consequences of the weak elliptic Harnack inequality.

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• The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis
• Energy inequalities for cutoff functions of p-energies on metric measures spaces

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