Riesz potential estimates for double obstacle problems with Orlicz growth

TL;DR

This paper investigates solutions to double obstacle problems with Orlicz growth involving measure data, establishing existence, gradient estimates via Riesz potentials, and criteria for $C^1$ regularity.

Contribution

It introduces new existence results and gradient estimates for double obstacle problems with Orlicz growth, advancing regularity theory in this context.

Findings

Existence of solutions in Orlicz-Sobolev spaces

Pointwise gradient estimates using Riesz potentials

C^1 regularity criterion established

Abstract

In this paper, we consider the solutions to the non-homogeneous double obstacle problems with Orlicz growth involving measure data. After establishing the existence of the solutions to this problem in the Orlicz-Sobolev space, we derive a pointwise gradient estimate for these solutions by Riesz potential, which leads to the result on the $C^1$ regularity criterion.