On the high regularity of solutions to the p-Laplacian boundary value problem in exterior domains

In this note, we consider the boundary value problem in exterior domains for the p-Laplacian system, p ∈ (1, 2). For suitable p and Lr -spaces, r > n, we furnish existence of a high-regular solution that is a solution whose second derivatives belong to L r (Ω ). Hence, in particular we get λ-Hölder continuity of the gradient of the solution, with λ = 1 − n/r Further, we improve previous results on W2,2-regularity in a bounded domain.