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Quasiconvexity at the Boundary, Positivity of the Second Variation and Elastic Stability

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The Breadth and Depth of Continuum Mechanics

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Abstract

For one dimensional problems of the calculus of variations, there is a well developed theory relating the positivity of the second variation at a critical point (i.e. ‘linearized stability’) to strong relative minima. These results, largely due to WEIERSTRASS, are usually proved by the method of ‘fields of extremals’ as is described in Bolza [1904] and Morrey [1966] or by an argument involving a careful use of Taylor series, as in Hestenes [1966, Chapter 3, § 14].

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Edinburgh, UK

    J. M. Ball & J. E. Marsden

  2. Department of Mathematics, University of California, Berkeley, USA

    J. M. Ball & J. E. Marsden

Authors
  1. J. M. Ball
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  2. J. E. Marsden
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Dedicated to Jerry Ericksen

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© 1986 Springer-Verlag Berlin Heidelberg

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Ball, J.M., Marsden, J.E. (1986). Quasiconvexity at the Boundary, Positivity of the Second Variation and Elastic Stability. In: The Breadth and Depth of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61634-1_22

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  • DOI: https://doi.org/10.1007/978-3-642-61634-1_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16219-3

  • Online ISBN: 978-3-642-61634-1

  • eBook Packages: Springer Book Archive

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