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 Holder continuity, up to the boundary.
- Quasilinear nonlocal operators
- fractional Sobolev spaces
- nonlocal tail
- Caccioppoli estimates
- obstacle problem