Boundary regularity and Hopf lemma for nondegenerate stable operators
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917792712753152 |
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| author | Grube, Florian |
| author_facet | Grube, Florian |
| contents | We prove sharp boundary H{ö}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional Laplacian. A Hopf-type boundary lemma is proven, too. An additional feature of this work is that the regularity estimate is robust as $s\to 1-$ and we recover the classical results for second order equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary regularity and Hopf lemma for nondegenerate stable operators Grube, Florian Analysis of PDEs 47G20, 35B65, 35S15, 35R09, 60G52 We prove sharp boundary H{ö}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional Laplacian. A Hopf-type boundary lemma is proven, too. An additional feature of this work is that the regularity estimate is robust as $s\to 1-$ and we recover the classical results for second order equations. |
| title | Boundary regularity and Hopf lemma for nondegenerate stable operators |
| topic | Analysis of PDEs 47G20, 35B65, 35S15, 35R09, 60G52 |
| url | https://arxiv.org/abs/2410.00829 |