Boundedness of Solutions to a Class of Coercive Systems with Morrey Data

TL;DR

This paper establishes the global boundedness of weak solutions to a class of coercive divergence form systems with nonlinearities governed by Morrey spaces, advancing understanding of solution regularity under complex growth conditions.

Contribution

It proves global boundedness for solutions of coercive quasilinear systems with Morrey space data, extending regularity results to more general nonlinear growth conditions.

Findings

Weak solutions are globally essentially bounded.

Solutions exhibit controlled growth with respect to Morrey space conditions.

The results apply to systems with componentwise coercivity and gradient growth control.

Abstract

We prove global essential boundedness for the weak solutions of divergence form quasilinear systems. The principal part of the differential operator is componentwise coercive and supports controlled growths with respect to the solution and its gradient, while the lower order term exhibits componentwise controlled gradient growth. The x-behaviour of the nonlinearities is governed in terms of Morrey spaces.