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, ItalyArshak Petrosyan
Department of Mathematics, Purdue University, West Lafayette, IN 47907, United StatesCamelia A. Pop
School of Mathematics, University of Minnesota, Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, United StatesMariana Smit Vega Garcia
Fakultät für Mathematik, Universität Duisburg–Essen, 45117 Essen, Germany
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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