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Homogenization of differential operators and integral functionals. Transl. from the Russian by G. A. Yosifian. (English) Zbl 0838.35001
Berlin: Springer-Verlag. xi, 570 p. (1994).
[For a review of the Russian original see Zbl 0801.35001.]
Although the titles of all chapters in this interesting book appear as well known, their contents are essentially new in comparison with the basic monographs of V. A. Marchenko and E. Ja. Khruslov, A. Bensoussan, J. L. Lions and L. Papanicolau, J. L. Lions, E. Sanchez-Palencia, N. S. Bahvalov and G. P. Panasenko, O. A. Oleinik, G. S. Shamaev and G. A. Yosifian. The authors consider new types of homogenization problems concerning differential operators with random coefficients, diffusion in random media, \(G\)-convergence, estimates of Hashin-Strikman type, stratified media, spectral problems, \(\Gamma\)-convergence, variational problems, plasticity etc. The stochastic point of view on composite structures is present in the most chapters. Without doubt, this book promotes an important new stage in the homogenization theory.

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
74E30 Composite and mixture properties
74E05 Inhomogeneity in solid mechanics