Parabolic systems with measurable coefficients in weighted Orlicz spaces (Q2796985)

This paper deals with the qualitative analysis of solutions of a class of Cauchy-Dirichlet problems with zero boundary data. The main purpose of this paper is to establish a global gradient estimate for weak solutions of this parabolic system with bounded measurable coefficients and whose nonhomogeneous term belongs to a suitable weighted Orlicz space. Under natural hypotheses, the central result of this paper proves that the spatial gradient of the weak solution gains the same Orlicz integrability as the nonhomogeneous term. This result is a Calderón-Zygmund type property in the setting of weighted Orlicz spaces.