The two-well problem in three dimensions

Georg Dolzmann; Bernd Kirchheim; Stefan Müller; Vladimir Šverák

doi:10.1007/PL00013455

The two-well problem in three dimensions

Georg Dolzmann, Bernd Kirchheim, Stefan Müller, Vladimir Šverák

School of Mathematics

Research output: Contribution to journal › Article › peer-review

14 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 language	English (US)
Pages (from-to)	21-40
Number of pages	20
Journal	Calculus of Variations and Partial Differential Equations
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/PL00013455
State	Published - Jan 2000

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The two-well problem in three dimensions

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