Weak Harnack inequality and Cartan property for nonlocal $W^{s,1}$-minimizers
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912977526980608 |
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| author | Lahti, Panu Li, Yuxin Nguyen, Khanh |
| author_facet | Lahti, Panu Li, Yuxin Nguyen, Khanh |
| contents | We establish a weak Harnack inequality for nonlocal $W^{s,1}$-subminimizers in a complete, connected, doubling metric measure space where $0<s<1$. As a corollary, we prove that $W^{s,1}$-subminimizers are semicontinuous, up to a suitable choice of pointwise representative. We then prove \emph{Cartan-type properties} for $W^{s,1}$-superminimizers. The theory turns out to be mostly analogous with the local case of BV super- and subminimizers. Our results seem to be new even in the classical Euclidean setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21121 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak Harnack inequality and Cartan property for nonlocal $W^{s,1}$-minimizers Lahti, Panu Li, Yuxin Nguyen, Khanh Analysis of PDEs Functional Analysis 35R11, 46E36 We establish a weak Harnack inequality for nonlocal $W^{s,1}$-subminimizers in a complete, connected, doubling metric measure space where $0<s<1$. As a corollary, we prove that $W^{s,1}$-subminimizers are semicontinuous, up to a suitable choice of pointwise representative. We then prove \emph{Cartan-type properties} for $W^{s,1}$-superminimizers. The theory turns out to be mostly analogous with the local case of BV super- and subminimizers. Our results seem to be new even in the classical Euclidean setting. |
| title | Weak Harnack inequality and Cartan property for nonlocal $W^{s,1}$-minimizers |
| topic | Analysis of PDEs Functional Analysis 35R11, 46E36 |
| url | https://arxiv.org/abs/2603.21121 |