Homogenization for Non-self-adjoint Periodic Elliptic Operators on an Infinite Cylinder
Nikita N. Senik · Functional Analysis and Its Applications · 2016
We consider an operator A ε on L 2( $${\mathbb{R}^{{d_1}}} \times {T^{{d_2}}}$$ ) (d 1 is positive, while d 2 can be zero) given by A ε = −div A(ε −1 x 1,x 2)∇, where A is periodic in the first variable and smooth in a sense in the second. We present approximations for (A ε − μ)−1 and ∇(A ε − μ)−1 (with appropriate μ) in the operator norm when ε is small. We also provide estimates for the rates of approximation that are sharp with respect to the order.