On the quasiconvex exposed points

Zhang, Kewei

ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 1-19

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.

Classification : 49J45, 49J10, 73V25
Keywords: quasiconvex functions, quasiconvex hull, homogeneous Young measure, quasiconvex exposed points, Straszewicz theorem

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