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On the quasiconvex exposed points

Published online by Cambridge University Press:  15 August 2002

Kewei Zhang
Kewei Zhang*
Affiliation:
School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, U.K.; [email protected].
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Abstract

The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.

Keywords

Quasiconvex functionsquasiconvex hullhomogeneous Young measurequasiconvex exposed pointsStraszewicz theorem.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 1 - 19
Copyright
© EDP Sciences, SMAI, 2001

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