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Quasiconvexity and related properties in the calculus of variations

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Generalized Convexity

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 405))

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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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Leipzig, Augustusplatz 10/11, D-04109, Leipzig, Germany

    H. Hartwig

Authors
  1. H. Hartwig
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Editor information

Editors and Affiliations

  1. Faculty of Economics, Janus Pannonius University, Rákóczi út 80, H-7621, Pécs, Hungary

    Sándor Komlósi

  2. Computer and Automation Institute, Hungary Academy of Sciences, P.O. Box 63, Kende u. 13-17, H-1518, Budapest, Hungary

    Tamás Rapcsák

  3. Graduate School of Management, University of California, 92521, Riverside, CA, USA

    Siegfried Schaible

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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

  • eBook Packages: Springer Book Archive

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