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


Canonical Formalism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations