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Rank-one convexity does not imply quasiconvexity

Published online by Cambridge University Press:  14 November 2011

Vladimír Šverák
Vladimír Šverák
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U.K. (On leave from MFF UK, Charles University, Prague, Czechoslovakia)
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Extract

We consider variational integrals

defined for (sufficiently regular) functions u: Ω→Rm. Here Ω is a bounded open subset of Rn, Du(x) denotes the gradient matrix of u at x and f is a continuous function on the space of all real m × n matrices Mm × n. One of the important problems in the calculus of variations is to characterise the functions f for which the integral I is lower semicontinuous. In this connection, the following notions were introduced (see [3], [9], [10]).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 1-2 , 1992 , pp. 185 - 189
Copyright
Copyright © Royal Society of Edinburgh 1992

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