# Boundedness of the solutions to nonlinear systems with Morrey data

## TL;DR

This paper proves that solutions to certain nonlinear elliptic systems with Morrey space data are bounded and have regular gradients, advancing understanding of their regularity properties under controlled growth conditions.

## Contribution

It establishes boundedness and Morrey regularity of solutions to nonlinear elliptic systems with Morrey space data, a novel result in this context.

## Key findings

- Weak solutions are essentially bounded.
- Gradients of solutions belong to Morrey spaces.
- Provides new regularity results for systems with Morrey data.

## Abstract

We consider nonlinear elliptic systems satisfying componentwise coercivity condition. The nonlinear terms have controlled growths with respect to the solution and its gradient, while the behaviour in the independent variable is governed by functions in Morrey spaces. We firstly prove essential boundedness of the weak solution and then obtain Morrey regularity of its gradient.