
Journal of Convex Analysis 19 (2012), No. 1, 063090 Copyright Heldermann Verlag 2012 Differentiabilty and Partial Hölder Continuity of Solutions of Nonlinear Elliptic Systems Giuseppe Floridia Dip. di Matematica e Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy floridia@dmi.unict.it Maria Alessandra Ragusa Dip. di Matematica e Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy maragusa@dmi.unict.it [Abstractpdf] The authors continue the study of regularity properties for solutions of elliptic systems started by M. A. Ragusa [(1) Local H\"older regularity for solutions of elliptic systems, Duke Mathematical Journal 113 (2002) 385397; (2) Continuity of the derivatives of solutions related to elliptic equations, Proc. Royal Society of Edinburgh 136(A) (2006) 10271039], proving, in a bounded open set $\Omega$ of ${\mathbb R}^n$, local differentiability and partial H\"older continuity of the weak solutions $u$ of nonlinear elliptic systems of order $2m$ in divergence form \begin{equation*} \sum_{\alpha\leq m}(1)^{\alpha} D^\alpha \, a^\alpha (x, Du) = 0. \end{equation*} Specifically, we generalize the results obtained by S. Campanato and P. Cannarsa [Differentiability and partial H\"older continuity of the solutions of nonlinear elliptic systems of order $2m$ with quadratic growth, Ann. Scuola Norm. Sup. Pisa (4)8 (1981) 285309] under the hypothesis that the coefficients $a^\alpha (x, Du)$ are strictly monotone with nonlinearity $q = 2$. Keywords: Higher order nonlinear elliptic systems, divergence form, monotone coefficients, generalized Sobolev spaces, local differentiability. MSC: 35J48, 35D10; 35J45, 35D30 [ Fulltextpdf (219 KB)] for subscribers only. 