The two-well problem in three dimensions

Journal article

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.

Authors: Dolzmann, G; Kirchheim, B; Muller, S; Sverak, V

• Publication status: Published
• Journal: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
• Volume: 10
• Issue: 1
• Pages: 21-40
• Publication date: 2000-01-01
• DOI: 10.1007/PL00013455
• ISSN: 0944-2669
• Language: English