Nonlocal Harnack inequality in a disconnected region
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918128942841856 |
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| author | Lee, Se-Chan |
| author_facet | Lee, Se-Chan |
| contents | We establish a Harnack inequality for weak solutions of nonlocal equations in a disconnected region. The inequality compares the value of a solution on one connected component with its value on another, capturing a purely nonlocal phenomenon with no local analogue. We provide two different approaches: one based on the localized maximum principle and another on the Poisson kernel estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal Harnack inequality in a disconnected region Lee, Se-Chan Analysis of PDEs 35B45, 35B65, 35R09 We establish a Harnack inequality for weak solutions of nonlocal equations in a disconnected region. The inequality compares the value of a solution on one connected component with its value on another, capturing a purely nonlocal phenomenon with no local analogue. We provide two different approaches: one based on the localized maximum principle and another on the Poisson kernel estimates. |
| title | Nonlocal Harnack inequality in a disconnected region |
| topic | Analysis of PDEs 35B45, 35B65, 35R09 |
| url | https://arxiv.org/abs/2508.16103 |