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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.12718 |
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| _version_ | 1866929699392847872 |
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| author | De Luca, Alessandra Felli, Veronica Vita, Stefano |
| author_facet | De Luca, Alessandra Felli, Veronica Vita, Stefano |
| contents | We provide fine asymptotics of solutions of fractional elliptic equations at boundary points where the domain is locally conical; that is, corner type singularities appear. Our method relies on a suitable smoothing of the corner singularity and an approximation scheme, which allow us to provide a Pohozaev type inequality. Then, the asymptotics of solutions at the conical point follow by an Almgren type monotonicity formula, blow-up analysis and Fourier decomposition on eigenspaces of a spherical eigenvalue problem. A strong unique continuation principle follows as a corollary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12718 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unique continuation from conical boundary points for fractional equations De Luca, Alessandra Felli, Veronica Vita, Stefano Analysis of PDEs 31B25, 35R11, 35C20, 35J75, 35A16 We provide fine asymptotics of solutions of fractional elliptic equations at boundary points where the domain is locally conical; that is, corner type singularities appear. Our method relies on a suitable smoothing of the corner singularity and an approximation scheme, which allow us to provide a Pohozaev type inequality. Then, the asymptotics of solutions at the conical point follow by an Almgren type monotonicity formula, blow-up analysis and Fourier decomposition on eigenspaces of a spherical eigenvalue problem. A strong unique continuation principle follows as a corollary. |
| title | Unique continuation from conical boundary points for fractional equations |
| topic | Analysis of PDEs 31B25, 35R11, 35C20, 35J75, 35A16 |
| url | https://arxiv.org/abs/2405.12718 |