Bauer's maximum principle and hulls of sets

Martin Kruzik

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Submission date: 31. May. 1999
Pages: 15
published in: Calculus of variations and partial differential equations, 11 (2000) 3, p. 321-332 
DOI number (of the published article): 10.1007/s005260000047
Bibtex
MSC-Numbers: 49R99
Keywords and phrases: bauer's maximum principle, extreme points, krein-milman theorem, polyconvexity, quasiconvexity, rank-one convexity, young measure
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Abstract:
We use the Bauer maximum principle for quasiconvex, polyconvex and rank- one convex functions to derive Krein-Milman-type theorems for compact sets in R^{m x n}. Further we show that in general a set of quasiconvex extreme points is not invariant under transposition and it is different from the set of rank-one convex extreme points.