Boundedness of the solutions to nonlinear 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.

12 pages

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