Solution of Interface Problems by Homogenization. I

The problem of an elliptic differential equation with nonsmooth coefficients is studied. It is assumed that the coefficients are double periodic with the period $H$ and the right-hand side is smooth. The behavior of the solution for $H \to 0$ is investigated and theorems about limiting solution are proved. The study is related to the homogenization ideas used in an intuitive way in the theory of nuclear reactors and theory of composite materials.