Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

• 成果类型: Article
• 署名作者: Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis
• 署名单位: University of Texas System; University of Texas Austin; Polytechnic University of Milan; New York University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0086-6
• 发表日期: 2008
• 页码: 425-461
• 关键词: degenerate

摘要

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary.