Daniela De Silva, Jean-Michel Roquejoffre
Published 2011-02-15, updated 2011-11-08Version 2
For a one-phase free boundary problem involving a fractional Laplacian, we prove that "flat free boundaries" are $C^{1,\alpha}$. We recover the regularity results of Caffarelli for viscosity solutions of the classical Bernoulli-type free boundary problem with the standard Laplacian.
Comments: Corrected some typos
A one-phase problem for the fractional Laplacian: regularity of flat free boundaries
Regularity of flat free boundaries for a $p(x)$-Laplacian problem with right hand side
An overdetermined problem in Riesz-potential and fractional Laplacian
![QR code for arXiv:1102.3086 [math.AP]](http://oss.arxitics.com/images/favicon.svg)