Higher differentiability and integrability for some nonlinear elliptic systems with growth coefficients in BMO

We consider local solutionsuof nonlinear elliptic systems of the type divA(x,Du)=divFin Omega subset of R-n where u:Omega -> R(N)is in a weightedW1,plocspace, with p >= 2,Fis in a weightedW1,2locspace andx -> A(x,xi)has growth coefficients in the space of functions with bounded meanoscillation. We prove higher differentiability of uin the sense that the nonlinear expression ofits gradientV mu(Du):=(mu 2+|Du|2)p-24Du, with 0<mu <= 1, is weakly differentiable with D(V mu(Du))in a weightedL2locspace. Moreover we derive some local Calder & oacute;n-estimates when the source term is not necessarily differentiable. Global estimates for a suitable Dirichlet problem are also available