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 Hölder continuity (up to the boundary), from the obstacle.
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 1 Jun 2016|
|MoE publication type||A1 Journal article-refereed|
- Primary: 35D10
- Secondary: 35B05