Homogenization of a boundary value problem in a periodically perforated domain (Q1866891)

The paper deals with the problem of averaging in a perforated domain with periodical structure. It is assumed that in each cavity two planes are located. A mixed boundary condition is given on the boundary of one plane, while a Dirichlet condition is prescribed on the boundary of the other plane. Both planes are of the so-called critical dimension. The author establishes a condition of weak convergence of the solution for the initial problem to the solution for the averaged problem.