Mathematics > Analysis of PDEs
[Submitted on 30 Aug 2025
(v1)
, last revised 3 Sep 2025 (this version, v2)]
Title: $C^{\infty}$ Regularity for the free boundary of one-phase Fractional Laplacian problem
Title: $C^{\infty}$一阶分数拉普拉斯问题自由边界的正则性
Abstract: We consider a one-phase free boundary problem involving fractional Laplacian $(-\Delta)^s$, $0<s<1$. D. De Silva, O. Savin, and Y. Sire proved that the flat boundaries are $C^{1,\alpha}$. We raise the regularity to $C^{\infty}$, extending the result known for $(-\Delta)^{1/2}$ by D. De Silva and O. Savin.
Submission history
From: Runcao Lyu [view email][v1] Sat, 30 Aug 2025 21:17:29 UTC (40 KB)
[v2] Wed, 3 Sep 2025 07:55:20 UTC (39 KB)
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