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Some remarks on quasiconvexity and rank-one convexity

Published online by Cambridge University Press:  14 November 2011

Pablo Pedregal
Pablo Pedregal
Affiliation:
ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain; Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
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Abstract

We explore some necessary conditions for quasiconvexity in an attempt to show that rank-one convexity does not imply quasiconvexity when the target space for deformations is two- dimensional. An interesting construction is presented, showing how rank-one directions may fit with each other, making the task harder than in higher dimensions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 5 , 1996 , pp. 1055 - 1065
Copyright
Copyright © Royal Society of Edinburgh 1996

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