Inserted: 18 dec 2015
Last Updated: 31 aug 2016
Journal: Calc. Var. Partial Differential Equations
Pages: Art. 63
We investigate the obstacle problem for a class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional $p$-Laplacian operator with measurable coefficients. Amongst other results, we will prove both the existence and uniqueness of the solutions to the obstacle problem, and that these solutions inherit regularity properties, such as boundedness, continuity and H\"older continuity (up to the boundary), from the obstacle.
Keywords: obstacle problem, fractional Sobolev spaces, Caccioppoli estimates, nonlocal tail, comparison estimates