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Holmbom, Anders; Silfver, Jeanette; Svanstedt, Nils; Wellander, Niklas

On two-scale convergence and related sequential compactness topics. (English) Zbl 1164.40304

Appl. Math., Praha 51, No. 3, 247-262 (2006).
Summary: A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of sequences of bounded functions in  \(L^{2}(\Omega )\) involving no periodicity assumptions. Further, the relation to the classical notion of compensated compactness and the recent concepts of two-scale compensated compactness and unfolding is discussed and a defect measure for two-scale convergence is introduced.

Cited in 6 Documents

MSC:

40A30 Convergence and divergence of series and sequences of functions

Keywords:

two-scale convergence; compensated compactness; two-scale transform; unfolding
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\textit{A. Holmbom} et al., Appl. Math., Praha 51, No. 3, 247--262 (2006; Zbl 1164.40304)
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