Gradient potential estimates for elliptic double obstacle problems with Orlicz growth

Abstract

In this paper,we consider the solutions of the elliptic double obstacle problems with Orlicz growth involving measure data. Some pointwise estimates for the approximable solutions to these problems are obtained in terms of fractional maximal operators. Furthermore, we establish pointwise and oscillation estimates for the gradients of solutions via the non-linear Wolff potentials, which in turn yield $C^{1,\hat{I}\pm }$-regularity of solutions.

arXiv admin note: substantial text overlap with arXiv:2104.00260