On homogenization procedure for periodic operators near the edge of an internal gap

(0.4) lim ε→0 uε = u. An extensive body of literature is devoted to homogenization problems. In the first place, the books [1]–[3] should be mentioned. Homogenization has different aspects (e.g., constructing the power series expansion in ε for uε − u, or estimating the error in (0.4)). The class of periodic problems of mathematical physics that are studied in the homogenization theory is quite extensive.