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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2509.00609 |
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| _version_ | 1866914018335129600 |
|---|---|
| author | Lyu, Runcao |
| author_facet | Lyu, Runcao |
| contents | We consider a one-phase free boundary problem involving fractional Laplacian $(-Δ)^s$, $0<s<1$. D. De Silva, O. Savin, and Y. Sire proved that the flat boundaries are $C^{1,α}$. We raise the regularity to $C^{\infty}$, extending the result known for $(-Δ)^{1/2}$ by D. De Silva and O. Savin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00609 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C^{\infty}$ Regularity for the free boundary of one-phase Fractional Laplacian problem Lyu, Runcao Analysis of PDEs We consider a one-phase free boundary problem involving fractional Laplacian $(-Δ)^s$, $0<s<1$. D. De Silva, O. Savin, and Y. Sire proved that the flat boundaries are $C^{1,α}$. We raise the regularity to $C^{\infty}$, extending the result known for $(-Δ)^{1/2}$ by D. De Silva and O. Savin. |
| title | $C^{\infty}$ Regularity for the free boundary of one-phase Fractional Laplacian problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.00609 |