Homogenization of the Neumann problem for higher order elliptic equations with periodic coefficients

Let O subset of R-d be a bounded domain of class C-2p. In L-2(O;C-n), we study a self-adjoint strongly elliptic operator A(N,epsilon) of order 2p given by the expression b(D)*g(x/epsilon)b(D), epsilon > 0, with Neumann boundary conditions. Here, g(x) is a bounded and positive definite matrix-valued function in R-d, periodic with respect to some lattice; b(D) = Sigma(vertical bar alpha vertical bar=p) b(alpha)D(alpha) is a differential operator of order p. The symbol b(xi) is subject to some condition ensuring strong ellipticity of the operator A(N,epsilon). We find approximations for the resolvent (A(N,epsilon )- zeta l) in different operator norms with error estimates depending on epsilon and zeta.