Differentiability of solutions of nonlinear elliptic systems of order 2m

The authors investigate differentiability in generalized Sobolev Spaces of the solutions of nonlinear parabolic systems of order $2\,m \,$ in divergence form of the following type \begin{equation*}%\label{eq01} \sum_{|\alpha|\leq m }(-1)^{|\alpha|} D^\alpha \, a^\alpha \left(X, Du \right)\,+\,\frac{\partial\,u }{\partial\,t} = 0. \end{equation*} The results are achieved inspired by the paper \cite{mama08} and the methods there applied. This note can be viewed as a continuation of the study of regularity properties for solutions of systems started in \cite{FR2}, \cite{duke}, \cite{dcds} and continued in \cite{FR3} and also as a generalization of the paper \cite{FR2} where regularity properties of the solutions of nonlinear elliptic systems with quadratic growth are reached.