On the quasiconvex exposed points
School of Mathematical Sciences, University of Sussex,
Falmer, Brighton BN1 9QH, U.K.; firstname.lastname@example.org.
Revised: 27 August 1999
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.
Mathematics Subject Classification: 49J45 / 49J10 / 73V25
Key words: Quasiconvex functions / quasiconvex hull / homogeneous Young measure / quasiconvex exposed points / Straszewicz theorem.
© EDP Sciences, SMAI, 2001