A one-phase problem for the fractional Laplacian: regularity of flat free boundaries

Abstract

We consider a one-phase free boundary problem involving a fractional Laplacian $(-Δ)^α$, $0<α<1,$ and we prove that ``flat free boundaries" are $C^{1,γ}$. We thus extend the known result for the case $α=1/2.$

arXiv admin note: substantial text overlap with arXiv:1102.3086