aequationes mathematicae

, Volume 5, Issue 1, pp 85–102 | Cite as

A canonical formalism for the non-parametric multiple-integral problem of Lagrange in the calculus of variations

  • S. P. Lipshitz
Research Papers

Keywords

Canonical Formalism 

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References

  1. [1]
    Carathéodory, C.,Die Methode der geodätischen Äquidistanten und das Problem von Lagrange, Acta Math.47, 199–236 (1926).Google Scholar
  2. [2]
    Carathéodory, C.,Über die Variationsrechnung bei mehrfachen Integralen, Acta Sci. Math. Szeged4, 193–216 (1929).Google Scholar
  3. [3]
    De Donder, Th.,Théorie invariantive du calcul des variations, new ed. (Gauthier-Villars, Paris 1935).Google Scholar
  4. [4]
    Marcus, M. andMinc, H.,A Survey of Matrix Theory and Matrix Inequalities (Allyn and Bacon, Boston 1964).Google Scholar
  5. [5]
    Rund, H.,The Hamilton-Jacobi Theory in the Calculus of Variations (Van Nostrand, London and New York 1966).Google Scholar
  6. [6]
    Rund, H.,A Canonical Formalism for Multiple Integral Problems in the Calculus of Variations, Aequationes Math.3, 44–63 (1969).Google Scholar
  7. [7]
    Weber, H. R.,Canonical Theory of the Nonparametric Lagrangian Multiple Integral Problems with Variable Boundaries, Bull. Amer. Math. Soc.75, 460–464 (1969).Google Scholar
  8. [8]
    Weyl, H.,Observations on Hilbert's Independence Theorem and Born's Quantization of Field Equations, Phys. Rev. (2)46, 505–508 (1934).Google Scholar
  9. [9]
    Weyl, H.,Geodesic Fields in the Calculus of Variations for Multiple Integrals, Ann. of Math. (2)36, 607–629 (1935).Google Scholar

Copyright information

© Birkhäuser Verlag 1970

Authors and Affiliations

  • S. P. Lipshitz
    • 1
  1. 1.University of the WitwatersrandJohannesburgSouth Africa

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