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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
68/2002

Rank-one convexity implies quasiconvexity on certain hypersurfaces

Nirmalendu Chaudhuri and Stefan Müller

Abstract

We show that, if $f : \Bbb M^{2\times 2}\longrightarrow \Bbb R$ is rank-1 convex on the hyperboloid $$H^{-}_{D}:=\left\{X\in S^{2\times 2}\, : \, \text{det}\,X=-D, X_{11}\geq c>0\right\}, D\geq 0, S^{2\times 2}$$ is the set of $2\times2$ real symmetric matrices, then $f$ can be approximated by quasiconvex functions on $\Bbb M^{2\times 2}$ uniformly on compact subsets of $H^{-}_{D}$. Equivalently, every gradient Young measure supported on a compact subset of $H^{-}_{D}$ is a laminate.

Received:
Aug 9, 2002
Published:
Aug 9, 2002

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