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Rank-one convexity implies quasi-convexity on certain hypersurfaces

Published online by Cambridge University Press:  12 July 2007

Nirmalendu Chaudhuri  and
Stefan Müller
Nirmalendu Chaudhuri
Affiliation:
Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22–26, 04103 Leipzig, Germanychaudhur@mis.mpg.de
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Abstract

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We show that, if f : M2×2 → R is rank-one convex on the hyperboloid is the set of 2 × 2 real symmetric matrices, then f can be approximated by quasi-convex functions on M2×2 uniformly on compact subsets of . Equivalently, every gradient Young measure supported on a compact subset of is a laminate.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 6 , December 2003 , pp. 1263 - 1272
Copyright
Copyright © Royal Society of Edinburgh 2003