Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift

Nicola Garofalo, Arshak Petrosyan, Camelia A. Pop, Mariana Smit Vega Garcia

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We establish the C1+γ-Hölder regularity of the regular free boundary in the stationary obstacle problem defined by the fractional Laplace operator with drift in the subcritical regime. Our method of the proof consists in proving a new monotonicity formula and an epiperimetric inequality. Both tools generalizes the original ideas of G. Weiss in [15] for the classical obstacle problem to the framework of fractional powers of the Laplace operator with drift. Our study continues the earlier research [12], where two of us established the optimal interior regularity of solutions.

Original languageEnglish (US)
Pages (from-to)533-570
Number of pages38
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume34
Issue number3
DOIs
StatePublished - May 1 2017

Keywords

  • Epiperimetric inequality
  • Fractional Laplacian with drift
  • Free boundary regularity
  • Monotonicity formulas
  • Obstacle problem
  • Symmetric stable process

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