Cα-regularity for a class of non-diagonal elliptic systems with p-growth

We consider weak solutions to nonlinear elliptic systems in aW(1,p)-setting which arise as Euler equations to certain variational problems. The solutions are assumed to be stationary in the sense that the differential of the variational integral vanishes with respect to variations of the dependent and independent variables. We impose new structure conditions on the coefficients which yield everywhere C-alpha-regularity and global C-alpha-estimates for the solutions. These structure conditions cover variational integrals like integral F(del u) dx with potential F(del u) := (F) over tilde (Q1(del u), ..., QN(del u)) and positively definite quadratic forms in del u defined as Q(i) (del u) = Sigma(alpha beta)a(i)(alpha beta)del u(alpha).del u(beta). A simple example consists in (F) over tilde (xi(1), xi(2)) := |xi(1)|(p/2) +|xi(2)|(p/2) or (F) over tilde(xi(1), xi(2)) := |xi(1)|(p/4) +|xi(2)|(p/4) . Since the Qi need not to be linearly dependent our result covers a class of nondiagonal, possibly nonmonotone elliptic systems. The proof uses a new weighted norm technique with singular weights in an L-p-setting.