Natural second-order regularity for parabolic systems with operators having (p,δ)-structure and depending only on the symmetric gradient

In this paper we consider parabolic problems with stress tensor depending only on the symmetric gradient. By developing a new approximation method (which allows to use energy-type methods typical for linear problems) we provide an approach to obtain global regularity results valid for general potential operators with (p,delta)-structure, for all p>1 and for all delta>0. In this way we prove ``natural'' second order spatial regularity -- up to the boundary -- in the case of homogeneous Dirichlet boundary conditions. The regularity results, are presented with full details for the parabolic setting in the case p>2. However, the same method also yields regularity in the elliptic case and for 1