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

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

2007-02-13

arxiv.org/abs/math/0702392v1

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00222-007-0086-6

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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