[Author]
 Senik N. N.

[Title]
 Homogenization for the Periodic Elliptic Second Order Differential Operator
 in a Strip with Various Boundary Conditions

[AMS Subj-class]
 35B27 Homogenization; partial differential equations in media
       with periodic structure

[Abstract]
 The paper concerns homogenization for the elliptic operator in $ L_2(\Pi) $,
 $ \Pi=\R \times (0, a) $, defined by the differential expression
 $ B_{\lambda}^{\epsilon} = \sum_{j = 1}^{2} D_j g_j(x_1 / \epsilon, x_2) D_j
 + \sum_{j = 1}^{2} (h_j(x_1 / \epsilon, x_2) D_j + D_j h_j^*(x_1 / \epsilon, x_2))
 + Q(x_1 / \epsilon, x_2\) + \lambda Q_*(x_1 / \epsilon, x_2) $
 with periodic, Neumann or Dirichlet boundary conditions. All the coefficients are
 assumed to be periodic of period 1 with respect to the first variable. Sharp-order
 approximations for the inverse of $ B_{\lambda}^{\epsilon} $ in the operator
 norms (from $ L_2 (\Pi) $ to $ L_2 (\Pi) $) and (from $ L_2 (\Pi) $ to $ H^1 (\Pi) $)
 are obtained, with error terms being $ O(\epsilon) $.

[Keywords]
 homogenization, operator error estimates, periodic differential operators,
 effective operator, corrector

[Comments]
 Russian, 52 pp.

[Contact e-mail]
 N.N.Senik@gmail.com