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On the rate of convergence for perforated plates with a small interior Dirichlet zone. (English) Zbl 1264.74189
Summary: The aim of the paper is to compare the asymptotic behavior of solutions of two boundary value problems for an elliptic equation posed in a thin periodically perforated plate. In the first problem, we impose homogeneous Dirichlet boundary condition only at the exterior lateral boundary of the plate, while at the remaining part of the boundary Neumann condition is assigned. In the second problem, Dirichlet condition is also imposed at the surface of one of the holes. Although in these two cases, the homogenized problem is the same, the asymptotic behavior of solutions is rather different. In particular, the presence of perturbation in the boundary condition in the second problem results in logarithmic rate of convergence, while for non-perturbed problem the rate of convergence is of power-law type.

74Q05 Homogenization in equilibrium problems of solid mechanics
74K20 Plates
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
Full Text: DOI
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