Gradient potential estimates in non-linear elliptic obstacle problems with measure data

In this paper, we derive pointwise estimates for the gradients of solutions to elliptic obstacle problems of p-Laplace-type with measure data. Moreover, we address a borderline problem in the regularity theory and give a sharp criterion for continuity of the gradient of a solution. Other applications are Lorentz space estimates for the gradient and a criterion for C1,α-regularity of solutions. © 2012 Elsevier Inc. All rights reserved.