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Lack of compactness in two-scale convergence. (English) Zbl 1112.35016
The authors prove that the div-curl condition implies some compactness in the two-scale convergence process (as in the classical case), when the oscillations of the sequences are faster than 1/\(\varepsilon\). Also, they give a counterexample showing that this is not the case for general sequences.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35B40 Asymptotic behavior of solutions to PDEs
49J45 Methods involving semicontinuity and convergence; relaxation
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