$C^{\infty}$ Regularity for the free boundary of one-phase Fractional Laplacian problem
Runcao Lyu
Published: 2025/8/30
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.