On Homogenization for Non-Self-Adjoint Periodic Elliptic Operators on an Infinite Cylinder

We consider an operator A (epsilon) on L (2)() (d (1) is positive, while d (2) can be zero) given by A (epsilon) = -div A(epsilon (-1) x (1),x (2))a double dagger, where A is periodic in the first variable and smooth in a sense in the second. We present approximations for (A (epsilon) - mu)(-1) and a double dagger(A (epsilon) - mu)(-1) (with appropriate mu) in the operator norm when epsilon is small. We also provide estimates for the rates of approximation that are sharp with respect to the order.