On the structure of quasiconvex hulls

Zhang, Kewei (1998) On the structure of quasiconvex hulls. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 15 (6). pp. 663-686. ISSN 0294-1449

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We define the set Kq,e ⊂ K of quasiconvex extreme points for compact sets K ⊂ MN×n and study its properties. We show that Kq,e is the smallest generator of Q(K)-the quasiconvex hull of K, in the sense that Q(Kq,e) = Q(K), and that for every compact subset W ⊂ Q(K) with Q(W) = Q(K), Kq,e ⊂ W. The set of quasiconvex extreme points relies on K only in the sense that View the MathML source. We also establish that Ke ⊂ Kq,e, where Ke is the set of extreme points of C(K)-the convex hull of K. We give various examples to show that Kq,e is not necessarily closed even when Q(K) is not convex; and that for some nonconvex Q(K), Kq,e = Ke. We apply the results to the two well and three well problems studied in martensitic phase transitions.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Kewei Zhang
Date Deposited: 06 Feb 2012 18:32
Last Modified: 09 Jul 2012 11:14
URI: http://sro.sussex.ac.uk/id/eprint/17025
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