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Does rank-one convexity imply quasiconvexity? (English) Zbl 0613.49014

Metastability and incompletely posed problems, Proc. Workshop, Minneapolis/Minn. 1984/85, IMA Vol. Math. Appl. 3, 17-32 (1987).
[For the entire collection see Zbl 0604.00008.]
This paper is devoted to investigate the relation between quasiconvexity and rank-one convexity. Essentially it is proved that rank-one convexity is a necessary but not sufficient condition for quasiconvexity.
Reviewer: R.Schianchi

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
26B25 Convexity of real functions of several variables, generalizations

Citations:

Zbl 0604.00008