Inventiones mathematicae

, Volume 171, Issue 2, pp 425–461

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

Article

Abstract

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.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Luis A. Caffarelli
    • 1
  • Sandro Salsa
    • 2
  • Luis Silvestre
    • 3
  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA
  2. 2.Department of MathematicsPolytechnic Institute of MilanMilanItaly
  3. 3.Courant Institute of Mathematical SciencesNew YorkUSA

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