Homogenization of Second Order Elliptic Operators with Periodic Coefficients

This chapter is intended to give a thorough description of the model homogenization problem. The fundamental homogenization theorem is proved here by two methods, viz., the method of compensated compactness and that of asymptotic expansions. Numerous examples are given to illustrate the computation of the homogenized matrix. Apart from the standard results of the homogenization theory, usually recorded in monographic literature, we consider here such questions as the derivation of explicit formulas in two-dimensional problems, residual diffusion, estimates for the homogenized matrix.