Regularity in a one-phase free boundary problem for the fractional Laplacian期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Regularity in a one-phase free boundary problem for the fractional Laplacian

Authors:	D De Silva JM Roquejoffre

Institution:	1. Department of Mathematics, Barnard College, Columbia University, New York, NY 10027, United States;2. Institut de Mathematiques (UMR CNRS 5640), Université Paul Sabatier, 31062 Toulouse Cedex 4, France

Abstract:	For a one-phase free boundary problem involving a fractional Laplacian, we prove that “flat free boundaries” are C^1,α $C^{1, α}$ . We recover the regularity results of Caffarelli for viscosity solutions of the classical Bernoulli-type free boundary problem with the standard Laplacian.

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