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2002
Issue 68

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MiS Preprint

68/2002

Rank-one convexity implies quasiconvexity on certain hypersurfaces

Nirmalendu Chaudhuri and Stefan Müller

Abstract

We show that, if $f : M^{2 \times 2} ⟶ R$ is rank-1 convex on the hyperboloid $H_{D}^{-} := {X \in S^{2 \times 2} : det X = - D, X_{11} \geq c > 0}, D \geq 0, S^{2 \times 2}$ is the set of $2 \times 2$ real symmetric matrices, then $f$ can be approximated by quasiconvex functions on $M^{2 \times 2}$ uniformly on compact subsets of $H_{D}^{-}$ . Equivalently, every gradient Young measure supported on a compact subset of $H_{D}^{-}$ is a laminate.

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Received:: 09.08.02

Published:: 09.08.02

Related publications

inJournal

2003 Repository Open Access

Nirmalendu Chaudhuri and Stefan Müller

Rank-one convexity implies quasi-convexity on certain hypersurfaces

In: Proceedings of the Royal Society of Edinburgh / A, 133 (2003) 6, pp. 1263-1272

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