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 delta-Reifenberg flat for delta > 0 small and the given Young function satisfies some moderate growth condition. As a corollary we obtain an optimal global W-2,W-p regularity for such a system. (C) 2009 Elsevier Inc. All rights reserved.