Hessian estimates in Orlicz spaces for fourth-order parabolic systems in non-smooth domains

We establish the global Hessian estimate in Orlicz spaces for a fourth-order parabolic system with discontinuous tensor coefficients in a non-smooth domain under the assumptions that the coefficients have small weak BMO semi-norms, the boundary of a domain is δ-Reifenberg flat for δ>0 small and the given Young function satisfies some moderate growth condition. As a corollary we obtain an optimal global W2,p regularity for such a system.