Zhang, Kewei (1998) On the structure of quasiconvex hulls. Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire, 15 (6). pp. 663-686. ISSN 0294-1449
Full text not available from this repository.Abstract
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 |
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Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
Depositing User: | Kewei Zhang |
Date Deposited: | 06 Feb 2012 18:32 |
Last Modified: | 26 Apr 2021 14:13 |
URI: | http://sro.sussex.ac.uk/id/eprint/17025 |