Wolff potentials and measure data vectorial problems with Orlicz growth

TL;DR

This paper investigates solutions to measure data elliptic systems with Orlicz growth, providing pointwise estimates via nonlinear Wolff-type potentials, extending recent results for p-Laplace systems to more general operators.

Contribution

It introduces a framework for analyzing elliptic systems with Orlicz growth, deriving pointwise estimates using Wolff potentials, and generalizing results beyond p-Laplace systems.

Findings

Established pointwise estimates for solutions using Wolff potentials.

Extended sharp results from p-Laplace systems to Orlicz growth operators.

Covered a broad class of operators with similar structure and growth conditions.

Abstract

We study solutions to measure data elliptic systems with Uhlenbeck-type structure that involve operator of divergence form, depending continuously on the spacial variable, and exposing doubling Orlicz growth with respect to the second variable. Pointwise estimates for the solutions that we provide are expressed in terms of a nonlinear potential of generalized Wolff type. Not only we retrieve the recent sharp results proven for $p$-Laplace systems, but additionally our study covers the natural scope of operators with similar structure and natural class of Orlicz growth.