Geodesic
Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 3, pp. 533-570

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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.

DOI : 10.1016/j.anihpc.2016.03.001
Classification : 35R35, 60G22
Keywords: Obstacle problem, Fractional Laplacian with drift, Free boundary regularity, Monotonicity formulas, Epiperimetric inequality, Symmetric stable process 
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     author = {Garofalo, Nicola and Petrosyan, Arshak and Pop, Camelia A. and Smit Vega Garcia, Mariana},
     title = {Regularity of the free boundary for the obstacle problem for the fractional {Laplacian} with drift},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {533--570},
     publisher = {Elsevier},
     volume = {34},
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Garofalo, Nicola; Petrosyan, Arshak; Pop, Camelia A.; Smit Vega Garcia, Mariana. Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 3, pp. 533-570. doi: 10.1016/j.anihpc.2016.03.001

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