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arXiv · 2605.15479

A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities

Caoxu Huang·Guanhua Liu
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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.

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Caoxu Huang, Guanhua Liu. 2026-05-14. A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities. https://arxiv.org/abs/2605.15479

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