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Multiscale homogenization of monotone operators. (English) Zbl 1156.35314

Summary: We prove a generalization of the iterated homogenization theorem for monotone operators, proved by J.-L.Lions, D. Lukkassen, L.-E. Persson and P. Wall [C. R. Acad. Sci., Paris, Sér. I, Math. 330, No. 8, 675–680 (2000; Zbl 0953.35041); Chin. Ann. Math., Ser. B 22, No. 1, 1–12 (2001; Zbl 0979.35047)]. Our results enable us to homogenize more realistic models of multiscale structures.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35J60 Nonlinear elliptic equations
74Q15 Effective constitutive equations in solid mechanics
47H05 Monotone operators and generalizations
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