On the structure of quasiconvex hulls

  • Kewei Zhang

    Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS UK

Abstract

We define the set of quasiconvex extreme points for compact sets and study its properties. We show that is the smallest generator of -the quasiconvex hull of , in the sense that , and that for every compact subset with , . The set of quasiconvex extreme points relies on only in the sense that . We also establish that , where is the set of extreme points of -the convex hull of . We give various examples to show that is not necessarily closed even when is not convex; and that for some nonconvex , . We apply the results to the two well and three well problems studied in martensitic phase transitions.

Cite this article

Kewei Zhang, On the structure of quasiconvex hulls. Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998), no. 6, pp. 663–686

DOI 10.1016/S0294-1449(99)80001-8