Optimal Regularity for Fully Nonlinear Nonlocal Equations with Unbounded Source Terms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912015523512320 |
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| author | Prazeres, Disson S. dos Santos, Makson S. |
| author_facet | Prazeres, Disson S. dos Santos, Makson S. |
| contents | We prove optimal regularity estimates for viscosity solutions to a class of fully nonlinear nonlocal equations with unbounded source terms. More precisely, depending on the integrability of the source term $f \in L^p(B_1)$, we establish that solutions belong to classes ranging from $C^{σ-d/p}$ to $C^σ$, at critical thresholds. We use approximation techniques and Liouville-type arguments. These results represent a novel contribution, providing the first such estimates in the context of not necessarily concave nonlocal equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03216 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Regularity for Fully Nonlinear Nonlocal Equations with Unbounded Source Terms Prazeres, Disson S. dos Santos, Makson S. Analysis of PDEs We prove optimal regularity estimates for viscosity solutions to a class of fully nonlinear nonlocal equations with unbounded source terms. More precisely, depending on the integrability of the source term $f \in L^p(B_1)$, we establish that solutions belong to classes ranging from $C^{σ-d/p}$ to $C^σ$, at critical thresholds. We use approximation techniques and Liouville-type arguments. These results represent a novel contribution, providing the first such estimates in the context of not necessarily concave nonlocal equations. |
| title | Optimal Regularity for Fully Nonlinear Nonlocal Equations with Unbounded Source Terms |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.03216 |