The two-well problem in three dimensions

Georg Dolzmann, Bernd Kirchheim, Stefan Müller, Vladimir Šverák

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We study properties of generalized convex hulls of the set K = SO(3) ∪ SO(3)H with det H > 0. If K contains no rank-1 connection we show that the quasiconvex hull of K is trivial if H belongs to a certain (large) neighbourhood of the identity. We also show that the polyconvex hull of K can be nontrivial if H is sufficiently far from the identity, while the (functional) rank-1 convex hull is always trivial. If the second well is replaced by a point then the polyconvex hull is trivial provided that there are no rank-1 connections.

Original languageEnglish (US)
Pages (from-to)21-40
Number of pages20
JournalCalculus of Variations and Partial Differential Equations
Volume10
Issue number1
DOIs
StatePublished - Jan 2000

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