The asymptotic expansion of the solution of a boundary-value problem with rapidly alternating type of boundary conditions

We consider a boundary-value problem for the Poisson equation with rapidly alternating type of boundary conditions in a domain between two parallel hyperplanes. The solution of the problem is assumed to be 1-periodic with respect to all the coordinates but one. We construct the asymptotic expansion for the solution in powers of a small parameter characterizing the alteration frequency of the boundary conditon. We obtain an estimate for the remainder term. Bibliography: 16 titles. Dedicated to Olga Arsenievna Oleinik This research has been supported in part by the foundation “Cultural Initiative”, by the International Science Foundation (Grant MIEOOO), and by the Russian Foundation for Basic Research. Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19, pp. 000-000, 0000.