On homogenization for periodic elliptic second order differential operators in a strip

This paper concerns homogenization for the elliptic operator in L₂(Π), Π = R × (0,a), defined by the differential expression B_λ^ε = Σ_j=1² D_jg_j(x₁/ε, x₂) D_j + Σ_j=1² (h_j(x₁/ε, x₂) D_j + D_jh_j*(x₁/ε, x₂)) + Q(x₁/ε, x₂) + λQ_*(x₁/ε, x₂) with periodic, Neumann or Dirichlet boundary conditions. All the coefficients are assumed to be periodic of period 1 with respect to the first variable. Sharp-order approximations for the inverse of B_λε in the norms of B(L₂(Π)) and B(L₂(Π), H¹(Π)) are obtained, with error terms being O(ε).