Abstract
We study the homogenization problem for matrix strongly elliptic operators on L2(Rd)n of the form Aε=−divA(x,x/ε)∇. The function A is Lipschitz in the first variable and periodic in the second. We do not require that A⁎=A, so Aε need not be self-adjoint. In this paper we provide the first two terms of a uniform approximation for (Aε−μ)−1 and the first term of a uniform approximation for ∇(Aε−μ)−1 as ε→0. Primary attention is paid to proving sharp-order bounds on the errors of approximation.
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