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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:
35R35Free boundary problems for PDE
26A33Fractional derivatives and integrals (real functions)
35J25Second order elliptic equations, boundary value problems
35B65Smoothness and regularity of solutions of PDE
References:
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