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MiS Preprint
21/1999
The two-well problem in three dimensions
Georg Dolzmann, Bernd Kirchheim, Stefan Müller and Vladimír Šverák
Abstract
We study properties of generalized convex hulls of the set $K = SO(3) \cup SO3(H)$ with $detH > 0$. If K contains no rank-1 one 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.
