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Some remarks concerning quasiconvexity and strong convergence

Published online by Cambridge University Press:  14 November 2011

L. C. Evans  and
R. F. Gariepy
L. C. Evans
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, U.S.A.
R. F. Gariepy
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, KY 40506, U.S.A.
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Synopsis

We show that the weak convergence of a sequence of functions in a Sobolev space plus the convergence of appropriately quasiconvex “energies” imply, in fact, strong convergence. This assertion makes rigorous, for example, the heuristic principle that “quasiconvexity damps out oscillations in the gradients” of minimising sequences in the calculus of variations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 1-2 , 1987 , pp. 53 - 61
Copyright
Copyright © Royal Society of Edinburgh 1987

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