On the global regularity for nonlinear -systems of the -Laplacian type in space variables

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

“…We extend the proofs obtained with Crispo, [1], from the homogeneous to the non-homogeneous boundary value problem. We prove, under suitable hypothesis, W 2,q (Ω) regularity up to the boundary, for arbitrarily large values of q.…”

“…Actually, the results proved in Refs. [9,1] seem to be, in the non-scalar case, the first regularity results up to the boundary, for the second derivatives of solutions.…”

“…In the homogeneous case, ψ = 0, the above results were proved in [1]. We assume the reader is acquainted with this last reference since in the sequel we will often appeal to it, in order to avoid unnecessary repetitions.…”

“…Next we reproduce some comments, presented in [1], concerning the case p < 2. For N = 1, in [5] the author proves W 2,p loc -regularity for any p < 2.…”

“…Following [1], we start by proving Theorem 1.1 under this last assumption. Actually, in the sequel we restrict ourselves to showing the indispensable manipulations needed to easily reconstruct a complete proof, with the help of Ref.…”