The Nonlinear Stokes Problem with General Potentials Having Superquadratic Growth

We discuss partial regularity results concerning local minimizers ${u : \mathbb{R}^3 \supset \Omega \rightarrow \mathbb{R}^3}$ of variational integrals of the form $$\int\limits_{\Omega}\left\{h(|\varepsilon(w)|) - f \cdot w\right\}\,dx$$ defined on appropriate classes of solenoidal fields, where h is a N-function of rather general type. As a byproduct we obtain a theorem on partial C ¹-regularity for weak solutions of certain non-uniformly elliptic Stokes-type systems modelling generalized Newtonian fluids.