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Weak lower semicontinuity of polyconvex integrals

Published online by Cambridge University Press:  14 November 2011

Jan Malý
Jan Malý
Affiliation:
Faculty of Mathematics and Physics–KMA, Charles University, Sokolovská 83, 18600 Praha, Czech Republic
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Synopsis

Multiple integrals with polyconvex integrands are studied on the class of all sense-preserving diffeomorphisms from W1,p(Ω, Rn) where Ω is an open subset of Rn. They are proved to be sequentially weakly lower semicontinuous if 1 < p = n –1. An example is presented showing that a similar result is not valid if p <n –1.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 4 , 1993 , pp. 681 - 691
Copyright
Copyright © Royal Society of Edinburgh 1993

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