LAUSR

Abstract We study the homogenization problem for matrix strongly elliptic operators on L 2 ( R d ) n of the form A e = − div A ( x , x / e ) ∇ . The function A is Lipschitz in the first variable and periodic in the second. We do not require that A ⁎ = A , so A e need not be self-adjoint. In this paper we provide the first two terms of a uniform approximation for ( A e − μ ) − 1 and the first term of a uniform approximation for ∇ ( A e − μ ) − 1 as e → 0 . Primary attention is paid to proving sharp-order bounds on the errors of approximation.