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On the structure of quasiconvex hulls

journal contribution
posted on 2023-06-07, 20:27 authored by Kewei Zhang
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.

History

Publication status

  • Published

Journal

Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire

ISSN

0294-1449

Publisher

Elsevier

Issue

6

Volume

15

Page range

663-686

ISBN

0294-1449

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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