Polyconvex, quasiconvex and rank one convex functions
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.
KeywordsConvex Function Main Property Lower Semicontinuous Invariant Function Diagonal Matrice
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