A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities
Analysis of PDEs
2026-05-18 v1 Probability
Abstract
In this paper we construct a self-similar fractal configured as an infinitely branched tree and equip it with a regular self-similar Dirichlet form. We show anomalous behaviour of the mean exit time with respect to typical metric balls. Under properly selected self-similar measure, we further show the weak elliptic Harnack inequality holds but the strong analogue fails.
Cite
@article{arxiv.2605.15479,
title = {A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities},
author = {Caoxu Huang and Guanhua Liu},
journal= {arXiv preprint arXiv:2605.15479},
year = {2026}
}