English

$C^{\infty}$ Regularity for the free boundary of one-phase Fractional Laplacian problem

Analysis of PDEs 2025-09-04 v2

Abstract

We consider a one-phase free boundary problem involving fractional Laplacian (Δ)s(-\Delta)^s, 0<s<10<s<1. D. De Silva, O. Savin, and Y. Sire proved that the flat boundaries are C1,αC^{1,\alpha}. We raise the regularity to CC^{\infty}, extending the result known for (Δ)1/2(-\Delta)^{1/2} by D. De Silva and O. Savin.

Keywords

Cite

@article{arxiv.2509.00609,
  title  = {$C^{\infty}$ Regularity for the free boundary of one-phase Fractional Laplacian problem},
  author = {Runcao Lyu},
  journal= {arXiv preprint arXiv:2509.00609},
  year   = {2025}
}