Inserted: 26 mar 2016
Last Updated: 18 may 2016
Journal: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
We deal with the obstacle problem for a class of nonlinear integro-differential operators, whose model is the fractional $p$-Laplacian with measurable coefficients. In accordance with well-known results for the analog for the pure fractional Laplacian operator, the corresponding solutions inherit regularity properties from the obstacle, both in the case of boundedness, continuity, and Hölder continuity, up to the boundary.
Keywords: obstacle problem, fractional Sobolev spaces, quasilinear nonlocal operators, Caccioppoli estimates, nonlocal tail