  We consider the Dirichlet boundary value problem for nonlinear N-systems of
partial differential equations with p-growth, 1<p<2, in the n-dimensional case.
For clearness, we confine ourselves to a particularly representative case, the
well known p-laplacian system. We are interested in regularity results, up to
the boundary, for the second order derivatives of the solution. We prove
W^{2,q}-global regularity results, for arbitrarily large values of q. In turn,
the regularity achieved implies the Holder continuity of the gradient of the
solution. It is worth noting that we cover the singular case \mu=0. See Theorem
2.1 below.
