Calderón–Zygmund theory for nonlinear elliptic problems with irregular obstacles

We consider a nonhomogeneous elliptic problem with an irregular obstacle involving a discontinuous nonlinearity over an irregular domain in divergence form of p-Laplacian type, to establish the global Calderón–Zygmund estimate by proving that the gradient of the weak solution is as integrable as both the gradient of the obstacle and the nonhomogeneous term under the BMO smallness of the nonlinearity and sufficient flatness of the boundary in the Reifenberg sense. © 2012 Elsevier Inc. All rights reserved