Partial regularity for parabolic systems with VMO-coefficients

Abstract

In this article we establish a partial Holder continuity result for weak solutions of parabolic systems, where the nonlinear vector field \begin{document}$ A(\cdot) $\end{document} satisfies a standard \begin{document}$ p $\end{document} -growth condition and a non-degenerate ellipticity condition with respect to the gradient variable, while in the space-time variable \begin{document}$ z = (x,t) $\end{document} it verifies a VMO-type condition. Thus, no continuity in the space-time variable is assumed. The proof is based on the method of \begin{document}$ \mathcal{A} $\end{document} -caloric approximation, applied on suitably chosen intrinsic cylinders.