\(\varGamma \)-convergence of multiscale periodic functionals depending on the time-derivative and the curl operator (Q655507)
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scientific article; zbMATH DE number 5994360
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\varGamma \)-convergence of multiscale periodic functionals depending on the time-derivative and the curl operator |
scientific article; zbMATH DE number 5994360 |
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\(\varGamma \)-convergence of multiscale periodic functionals depending on the time-derivative and the curl operator (English)
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4 January 2012
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The author studies \(\Gamma\)-convergence of periodic multiscale integral functionals whose densities depend on the time derivative and on the curl of solenoidal fields. Under the assumption that the functionals are of a quadratic growth (uniformly), it is shown the existence of a \(\Gamma\)-limit. The limit (homogenized) density is expressed in terms of a certain variational cell problem. The proof makes use of multiscale Young measures.
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multiscale convergence
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divergence-free fields, multiscale Young measures
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periodic multiscale integral functionals
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variational cell problem
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