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On SO(n)-Invariant Rank 1 Convex Functions

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The Rational Spirit in Modern Continuum Mechanics

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Abstract

Let f be a function defined on the set n×n of all real square matrices of order n. If f is SO(n)-invariant, it has a representation \( \tilde f \) on ℝn through the signed singular values of the matrix argument A ∈ n×n. A necessary and sufficient condition for the rank 1 convexity of f in terms of \( \tilde f \) is given.

This research was supported by Grant 201/00/1516 of the Grant Agency of the Czech Republic.

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Authors and Affiliations

  1. Mathematical Institute of the AV ČR, Žitná 25, 115 67, Prague 1, Czech Republic

    M. Šilhavý

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  1. M. Šilhavý
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Editor information

Editors and Affiliations

  1. University of Kentucky, Lexington, USA

    Chi-Sing Man

  2. University of Minnesota, Minneapolis, USA

    Roger L. Fosdick

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In memory of Clifford Truesdell

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© 2004 Kluwer Academic Publishers

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Šilhavý, M. (2004). On SO(n)-Invariant Rank 1 Convex Functions. In: Man, CS., Fosdick, R.L. (eds) The Rational Spirit in Modern Continuum Mechanics. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2308-1_40

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  • DOI: https://doi.org/10.1007/1-4020-2308-1_40

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1828-2

  • Online ISBN: 978-1-4020-2308-8

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