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

摘要

This paper concerns homogenization for the elliptic operator in L2(Π), Π = ℝ × (0,a), defined by the differential expression equation 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 Bλε in the norms of B(L2(Π)) and B(L2(Π), H¹(Π)) are obtained, with error terms being O(ε).