Geodesic
On the eigenvalues of boundary value problems for the system of elasticity theory with rapidly oscillating coefficients in a~perforated domain
Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 505-519

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A mixed boundary value problem in a perforated domain is considered for the system of linear elasticity theory with nonuniformly oscillating coefficients. The coefficients of the system depend on fast and slow independent variables and are periodic functions of fast variables with period $\varepsilon$. For small $\varepsilon$, estimates are obtained for the difference between the eigenvalues of this problem and the eigenvalues of the corresponding averaged problem. Estimates of the same kind are obtained for eigenfunctions. The methods worked out in the paper are general, and they are applicable to a large class of problems on averaging of eigenvalues for equations and systems of elliptic type. Bibliography: 5 titles. 
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     author = {G. A. Iosif'yan and O. A. Oleinik and A. S. Shamaev},
     title = {On the eigenvalues of boundary value problems for the system of elasticity theory with rapidly oscillating coefficients in a~perforated domain},
     journal = {Sbornik. Mathematics},
     pages = {505--519},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_60_2_a15/}
}
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G. A. Iosif'yan; O. A. Oleinik; A. S. Shamaev. On the eigenvalues of boundary value problems for the system of elasticity theory with rapidly oscillating coefficients in a~perforated domain. Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 505-519. http://geodesic.mathdoc.fr/item/SM_1988_60_2_a15/