Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian

Juan Pablo Borthagaray, Ricardo H. Nochetto, Abner J. Salgado

Published 2018-06-21Version 1

We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle problem for the integral fractional Laplacian. The weight is a power of the distance to the boundary. These bounds then serve us as a guide in the design and analysis of an optimal finite element scheme over graded meshes.