JournalsaihpcVol. 34, No. 3pp. 533–570

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

  • Nicola Garofalo

    Dipartimento d'Ingegneria Civile e Ambientale (DICEA), Universitá di Padova, Via Trieste 63, 35131 Padova, Italy

  • Arshak Petrosyan

    Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States

  • Camelia A. Pop

    School of Mathematics, University of Minnesota, Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, United States

  • Mariana Smit Vega Garcia

    Fakultät für Mathematik, Universität Duisburg–Essen, 45117 Essen, Germany
Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift cover
Download PDF

Abstract

We establish the -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.

Cite this article

Nicola Garofalo, Arshak Petrosyan, Camelia A. Pop, Mariana Smit Vega Garcia, Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, pp. 533–570

DOI 10.1016/J.ANIHPC.2016.03.001