On the quasiconvex exposed points

Kewei Zhang

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 6, page 1-19
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Zhang, Kewei. "On the quasiconvex exposed points." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 1-19. <http://eudml.org/doc/197361>.

@article{Zhang2010,
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. },
author = {Zhang, Kewei},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Quasiconvex functions; quasiconvex hull; homogeneous Young measure; quasiconvex exposed points; Straszewicz theorem.; quasiconvexity; extreme points; material microstructures},
language = {eng},
month = {3},
pages = {1-19},
publisher = {EDP Sciences},
title = {On the quasiconvex exposed points},
url = {http://eudml.org/doc/197361},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Zhang, Kewei
TI - On the quasiconvex exposed points
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 6
SP - 1
EP - 19
AB - 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.
LA - eng
KW - Quasiconvex functions; quasiconvex hull; homogeneous Young measure; quasiconvex exposed points; Straszewicz theorem.; quasiconvexity; extreme points; material microstructures
UR - http://eudml.org/doc/197361
ER -

References

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