Higher differentiability for solutions of stationary p-Stokes systems

We consider weak solutions (Formula presented.) to stationary p-Stokes systems of the type (Formula presented.) in (Formula presented.), where the function (Formula presented.) satisfies p-growth conditions in ξ and depends Hölder continuously on x. By (Formula presented.) we denote the symmetric part of the gradient (Formula presented.) and we write (Formula presented.) for the convective term. In this setting, we establish results on the fractional higher differentiability of both the symmetric part of the gradient (Formula presented.) and of the pressure π. As an application, we deduce dimension estimates for the singular set of the gradient (Formula presented.), thereby improving known results on partial (Formula presented.) -regularity for solutions to stationary p-Stokes systems.