A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913131842764800 |
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| author | Huang, Caoxu Liu, Guanhua |
| author_facet | Huang, Caoxu Liu, Guanhua |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15479 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities Huang, Caoxu Liu, Guanhua Analysis of PDEs Probability 28A80, 31C25, 47D07, 60J46 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. |
| title | A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities |
| topic | Analysis of PDEs Probability 28A80, 31C25, 47D07, 60J46 |
| url | https://arxiv.org/abs/2605.15479 |