On homogenization of solutions of boundary value problems in domains, perforated along manifolds. (English) Zbl 1170.35320
Summary: The problem of homogenization of solutions to the Poisson equation in domains, perforated along a manifold, is considered with the Neumann boundary condition, with the Dirichlet boundary condition or the mixed condition on cavities. The same method can be applied also to boundary value problems in domains, perforated in some subdomains. We study here also the corresponding spectral problems. E. De Giorgi was one of the first mathematicians, who considered homogenization problems E. De Giorgi Boll. Unione Mat. Ital., IV, Ser. 8, 391–411 (1973; Zbl 0274.35002)].
MSC:
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 35J25 | Boundary value problems for second-order elliptic equations |
Citations:
Zbl 0274.35002References:
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