Gradient potential estimates for elliptic double obstacle problems with Orlicz growth

TL;DR

This paper develops pointwise and oscillation estimates for solutions to elliptic double obstacle problems with Orlicz growth, leading to regularity results using fractional maximal operators and Wolff potentials.

Contribution

It introduces new pointwise and oscillation estimates for solutions with Orlicz growth, advancing regularity theory for obstacle problems with measure data.

Findings

Establishes pointwise estimates via fractional maximal operators.

Derives gradient oscillation estimates using Wolff potentials.

Proves $C^{1,\alpha}$-regularity of solutions.

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 $C^{1,\alpha}$-regularity of solutions.