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

Abstract

a b s t r a c tWe 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.