Polyconvex, quasiconvex and rank one convex functions

Part of the Applied Mathematical Sciences book series (AMS, volume 78)

We should again emphasize that in the scalar case all these notions are equivalent to the usual convexity condition. The definitions and main properties of these generalized notions of convexity are discussed in Section 5.2. In Section 5.3, we give several examples. In particular we show that all the reverse implications are false. Finally, in an appendix (Section 5.4), we gather certain elementary properties of determinants.


Convex Function Main Property Lower Semicontinuous Invariant Function Diagonal Matrice 
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© Springer Science+Business Media, LLC 2008

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