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

被引：19

作者：

Garofalo, Nicola ^{[1
]}

Petrosyan, Arshak ^{[2
]}

Pop, Camelia A. ^{[3
,5
]}

Garcia, Mariana Smit Vega ^{[4
]}

机构：

[1] Univ Padua, DICEA, Via Trieste 63, I-35131 Padua, Italy

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[3] Univ Minnesota, Sch Math, Vincent Hall,206 Church St SE, Minneapolis, MN 55455 USA

[4] Univ Duisburg Essen, Fak Math, D-45117 Essen, Germany

[5] Inst Math & Its Applicat, Lind Hall,207 Church St SE, Minneapolis, MN 55455 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2017年 / 34卷 / 03期

关键词：

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

D O I：

10.1016/j.anihpc.2016.03.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the C1+gamma-Holder 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. (C) 2016 Elsevier Masson SAS. All rights reserved.

引用

页码：533 / 570

页数：38

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