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

Daniela De Silva; Jean-Michel Roquejoffre

doi:10.1016/j.anihpc.2011.11.003

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

Analysis of PDEs 2016-01-20 v2

Authors: Daniela De Silva , Jean-Michel Roquejoffre

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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.

Keywords

free boundary problem fractional Laplacian regularity flat free boundaries viscosity solutions Bernoulli-type problem

Cite

@article{arxiv.1102.3086,
  title  = {Regularity in a one-phase free boundary problem for the fractional Laplacian},
  author = {Daniela De Silva and Jean-Michel Roquejoffre},
  journal= {arXiv preprint arXiv:1102.3086},
  year   = {2016}
}

Comments

Corrected some typos

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