The weak elliptic Harnack inequality revisited
Analysis of PDEs
2022-08-12 v1 Functional Analysis
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 Poincar\'{e} 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.
Cite
@article{arxiv.2208.05580,
title = {The weak elliptic Harnack inequality revisited},
author = {Jiaxin Hu and Zhenyu Yu},
journal= {arXiv preprint arXiv:2208.05580},
year = {2022}
}