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Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. (English) Zbl 1148.35097
Author’s summary: We use a characterization of the fractional Laplacian as a Dirichlet-to-Neumann operator for an approppriate 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.

MSC:
35R35 Free boundary problems for PDEs
26A33 Fractional derivatives and integrals
35J25 Boundary value problems for second-order elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
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