An implicit two-phase obstacle-type problem for the p-Laplacian with the fractional gradient

In this work we study an inhomogeneous two-phase obstacle-type problem associated to the s-fractional p-Laplacian. Besides the existence and uniqueness of solutions, we study the convergence of the solutions when s→ 1 to the classical problem. We also study the continuous dependence with respect to the level-set function v, yielding an existence result for a two-phase obstacle-type problem with an implicit level-set function.