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The two-well problem in three dimensions

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.
Publication status:
Published

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Publisher copy:
10.1007/PL00013455

Authors


Dolzmann, G More by this author
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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume:
10
Issue:
1
Pages:
21-40
Publication date:
2000-01-05
DOI:
ISSN:
0944-2669
URN:
uuid:3d1428c5-21e1-4c2e-aaf1-88d4d8b4f54f
Source identifiers:
5373
Local pid:
pubs:5373
Language:
English

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