Parabolic systems with measurable coefficients in weighted Orlicz spaces

Abstract

We consider a parabolic system in divergence form with measurable coefficients in a cylindrical space–time domain with nonsmooth base. The associated nonhomogeneous term is assumed to belong to a suitable weighted Orlicz space. Under possibly optimal assumptions on the coefficients and minimal geometric requirements on the boundary of the underlying domain, we generalize the Calderón–Zygmund theorem for such systems by essentially proving that the spatial gradient of the weak solution gains the same weighted Orlicz integrability as the nonhomogeneous term.