Gradient Riesz potential estimates for a general class of measure data quasilinear systems

TL;DR

This paper establishes gradient regularity estimates for solutions to measure data elliptic systems with Uhlenbeck-type structure and Orlicz growth, using Riesz potential techniques to relate data regularity to solution regularity.

Contribution

It introduces pointwise gradient estimates for measure data elliptic systems with complex growth conditions, extending regularity transfer results to a broad class of systems.

Findings

Gradient estimates in terms of Riesz potentials

Regularity transfer from data to solutions

Applicability to systems with Orlicz growth

Abstract

We study the gradient regularity of solutions to measure data elliptic systems with Uhlenbeck-type structure and Orlicz growth. For any bounded Borel measure, pointwise estimates for the gradient of solutions are provided in terms of the truncated Riesz potential. This allows us to show a precise transfer of regularity from data to solutions on various scales.