On the interior regularity of weak solutions to nonlinear elliptic systems of second order (Q1176631)

The author studies the interior \(C^{1,\alpha}\)-regularity for weak solutions \(u\) (i.e. \(Du\in\text{BMO})\) of the elliptic system \[ - \sum_{j=1}^ N D_ ja_{ij}(x,u,Du)+a_ i(x,u,Du)=-\sum_{j=1}^ N D_ jf_{ij}(x)+f_ i(x)\quad (i=1,\dots,n). \] This extends previous work of \textit{M. Giaquinta} and \textit{J. Nečas} [Commentat. Math. Univ. Carol. 20, 111-121 (1979; Zbl 0396.35047), or J. Reine Angew. Math. 316, 140-159 (1980; Zbl 0435.35036)].