On the global regularity for singular [formula omitted]-systems under non-homogeneous Dirichlet boundary conditions

Abstract

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 W2,q and C1,α regularity, up to the boundary, under suitable assumptions on the couple p,q. In particular, there is a constant K0, independent of p and q, such that our regularity results hold at least for q≤K0p−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.