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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.14305 |
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| _version_ | 1866914333865279488 |
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| author | Hakobyan, Aram Poghosyan, Michael Shahgholian, Henrik |
| author_facet | Hakobyan, Aram Poghosyan, Michael Shahgholian, Henrik |
| contents | We prove that the gradient of any bounded subharmonic function is upper semi-continuous, provided that its super-level sets can be touched from the exterior by uniform $C^{1,\text{Dini}}$ domains at every point. This idea extends to a class of general operators, as well as to the boundary behaviour of the gradient of solutions of the Dirichlet problem in a domain whose boundary satisfy this geometric condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14305 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Partial regularity of the gradient for subsolutions Hakobyan, Aram Poghosyan, Michael Shahgholian, Henrik Analysis of PDEs 35B65 We prove that the gradient of any bounded subharmonic function is upper semi-continuous, provided that its super-level sets can be touched from the exterior by uniform $C^{1,\text{Dini}}$ domains at every point. This idea extends to a class of general operators, as well as to the boundary behaviour of the gradient of solutions of the Dirichlet problem in a domain whose boundary satisfy this geometric condition. |
| title | Partial regularity of the gradient for subsolutions |
| topic | Analysis of PDEs 35B65 |
| url | https://arxiv.org/abs/2602.14305 |