### Abstract

We define the set K_{q,e} ? K of quasiconvex extreme points for compact sets K ? M^{N X n} and study its properties. We show that K_{q,e} is the smallest generator of Q(K)-the quasiconvex hull of K, in the sense that Q(K_{q,e}) = Q(K), and that for every compact subset W ? Q(K) with Q(W) = Q(K), K_{q,e} ? W. The set of quasiconvex extreme points relies on K only in the sense that Q(K)_{q,e} ? K_{q,e} ? [Q(K)_{q,e}]. We also establish that K_{e} ? K_{q,e}, where K_{e} is the set of extreme points of C(K)-the convex hull of K. We give various examples to show that K_{q,e} is not necessarily closed even when Q(K) is not convex; and that for some nonconvex Q(K), K_{q,e} = K_{e}. We apply the results to the two well and three well problems studied in martensitic phase transitions. © Elsevier, Paris.

Original language | English |
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Pages (from-to) | 663-686 |

Number of pages | 24 |

Journal | Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire |

Volume | 15 |

Issue number | 6 |

DOIs | |

Publication status | Published - Nov 1998 |

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## Cite this

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

*15*(6), 663-686. https://doi.org/10.1016/S0294-1449(99)80001-8