Continuity of solutions to equations with weakly singular nonlocal operators
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910852163043328 |
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| author | Jarohs, Sven Kassmann, Moritz Weth, Tobias |
| author_facet | Jarohs, Sven Kassmann, Moritz Weth, Tobias |
| contents | We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions are continuous, and we provide a uniform a-priori estimates for the modulus of continuity. In contrast to earlier works, we allow the nonlocal operators to be highly anisotropic and weakly singular, and we allow the associated kernel functions to vanish close to the singularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15337 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Continuity of solutions to equations with weakly singular nonlocal operators Jarohs, Sven Kassmann, Moritz Weth, Tobias Analysis of PDEs 35B65, 35R09, 47G20, 60J75 We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions are continuous, and we provide a uniform a-priori estimates for the modulus of continuity. In contrast to earlier works, we allow the nonlocal operators to be highly anisotropic and weakly singular, and we allow the associated kernel functions to vanish close to the singularity. |
| title | Continuity of solutions to equations with weakly singular nonlocal operators |
| topic | Analysis of PDEs 35B65, 35R09, 47G20, 60J75 |
| url | https://arxiv.org/abs/2311.15337 |