A One-Phase Problem for the Fractional Laplacian: Regularity of Flat Free Boundaries
by D. De Silva   O. Savin   Y. Sire  

Vol. 9 No. 1 (2014) P.111~P.145

ABSTRACT

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

KEYWORDS
Fractional laplacians, free boundary problems, viscosity methofs, improvement of flatness

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35B09, 35B50, 35J05, 35J60

MILESTONES

Received: 2013-11-28
Revised :
Accepted: 2013-12-16

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