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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.; k.zhang@sussex.ac.uk.
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Abstract

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

Keywords

Quasiconvex functionsquasiconvex hullhomogeneous Young measurequasiconvex exposedpointsStraszewicz theorem.

Information

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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