On the global regularity for singular -systems under non-homogeneous Dirichlet boundary conditions

We consider the non-homogeneous Dirichlet boundary value problem for elliptic, singular, p -systems of N equations in n space variables, 1 < p ≤ 2 . We prove W 2 , q and C 1 , α regularity, up to the boundary, under suitable assumptions on the couple p , q . In particular, there is a constant K 0 , independent of p and q , such that our regularity results hold at least for q ≤ K 0 p − 2 . The singular case μ = 0 is covered. We extend earlier results of the author and F. Crispo, from the homogeneous to the non-homogeneous case.