Differentiability and partial H\''older continuity of solutions of nonlinear elliptic systems

The authors continue the study of regularity properties for solutions of elliptic systems started in \cite{duke} and continued \cite{REdin}, proving, in a bounded open set $\Omega $ of $\rea^n, $ local differentiability and partial H\"older continuity of the weak solutions u of nonlinear elliptic systems of %second GF26/07/10 order $2m$ in divergence form \begin{equation*}%\label{eq01} \sum_{|\alpha|\leq m }(-1)^{|\alpha|} D^\alpha \, a^\alpha \left(x, %u, Du \right) = 0. \end{equation*} Specifically, are generalized the results obtained by Campanato and Cannarsa, contained in \cite{vm06}, % concerned with the problem m = 1, GF26/07/10 under the hypothesis that the coefficient $a^\alpha \left(x, Du \right),$ are strictly monotone with nonlinearity q = 2.