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. As a result, 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.

Elliptic obstacle problem; Dini-BMO coefficients; Wolff potential; Restricted fractional maximal function