Gradient potential estimates in elliptic obstacle problems with Orlicz growth

Abstract

In this paper,we consider the solutions of the non-homogeneous elliptic obstacle problems with Orlicz growth involving measure data. We first establish the pointwise estimates of the approximable solutions to these problems via fractional maximal operators. Furthermore, we obtain pointwise and oscillation estimates for the gradients of solutions by the non-linear Wolff potentials, and these yield results on \(C^{1,\alpha }\)-regularity of solutions.