Regularity in a one-phase free boundary problem for the fractional Laplacian

Abstract

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.

Corrected some typos

References in corpus (2)

• An extension problem related to the fractional Laplacian
• Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian

Cited by in corpus (3)

• Two-phase problems with distributed source: regularity of the free boundary
• Regularity of shape optimizers for some spectral fractional problems
• Minimizing Eigenvalues of the Fractional Laplacian