Calderon-Zygmund theory for asymptotically regular nonlinear elliptic problems with double obstacles

We study nonlinear elliptic double obstacles problems with an asymptotically regular nonlinearity in a non-smooth domain. Here, we obtain a global Calderon-Zygmund type estimate in the setting of Lorentz spaces by making use of the perturbation method. More precisely, we approximate the solutions of asymptotically regular double obstacles problems to the solutions of regular single obstacle problems when the gradients of solutions are close to infinity.