Several versions of the compensated compactness principle
Journal Article
·
· Sbornik. Mathematics
The convergence of the product of a solenoidal vector w{sub {epsilon}} and a gradient {nabla}u{sub {epsilon}} in L{sup 1}({Omega}) (where {Omega} is a region in R{sup d}) is investigated in the case when the factors converge weakly in the spaces L{sup {gamma}({Omega})}{sup d} and L{sup {alpha}({Omega})}{sup d}, respectively, with 1/{gamma}+1/{alpha}>1, which means that the main assumption of the classical div-curl lemma fails. Nevertheless, the same convergence (in the sense of distributions in {Omega}) as in the framework of the div-curl lemma, survives under certain additional assumptions. The new versions of the compensated compactness principle proved in the paper can be used in homogenization and in the theory of G-convergence of monotone operators with non-standard coercivity and growth properties, for instance, some degenerate operators. Bibliography: 20 titles.
- OSTI ID:
- 21612604
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 9 Vol. 202; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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