Abstract
This paper deals with relationships between polyconvexity, Morrey’s quasi-convexity and rank one convexity. These generalized convexity properties of functions on the space of all m × n matrices play an important role in the vectorial calculus of variations. We present a characterization of rank one convex functions via their extension from a nonconvex subset of the minor space to the whole space and introduce a weakened polyconvexity condition which implies quasiconvexity. The results are illustrated by examples.
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© 1994 Springer-Verlag Berlin Heidelberg
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Hartwig, H. (1994). Quasiconvexity and related properties in the calculus of variations. In: Komlósi, S., Rapcsák, T., Schaible, S. (eds) Generalized Convexity. Lecture Notes in Economics and Mathematical Systems, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46802-5_7
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DOI: https://doi.org/10.1007/978-3-642-46802-5_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57624-2
Online ISBN: 978-3-642-46802-5
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