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Averaging in a perforated domain with an oscillating third boundary condition. (English. Russian original) Zbl 1030.35008

Sb. Math. 192, No. 7, 933-949 (2001); translation from Mat. Sb. 192, No. 7, 3-20 (2001).
The authors consider the homogenization of the Poisson problem in an \(\varepsilon\)-periodic perforated domain with a Fourier condition on the boundary of the holes. Assuming that the coefficients of the Fourier condition are regular and that the corresponding averages are small, they prove that the two leading terms of the asymptotic expansion of the solution provide a precision of order \(\sqrt{\varepsilon}\) in the \(H^1\)-norm.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
49J45 Methods involving semicontinuity and convergence; relaxation
35J25 Boundary value problems for second-order elliptic equations
74Q05 Homogenization in equilibrium problems of solid mechanics
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