Boundedness of solutions to a class of coercive systems with Morrey data

Abstract

We prove global essential boundedness of the weak solutions u∈W01,p(Ω;RN) to the quasilinear system div,(A(x,u,Du))=b(x,u,Du). The principal part A(x,u,Du) of the differential operator is componentwise coercive and supports controlled growths with respect to u and Du, while the lower order term b(x,u,Du) exhibits componentwise controlled gradient growth. The x-behaviour of the nonlinearities is governed in terms of Morrey spaces.