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Solution of the inverse problem of the calculus of variations


Author: Jesse Douglas
Journal: Trans. Amer. Math. Soc. 50 (1941), 71-128
MSC: Primary 49.0X
DOI: https://doi.org/10.1090/S0002-9947-1941-0004740-5
MathSciNet review: 0004740
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  • [1] G. Darboux, Leçons sur la Théorie Générale des Surfaces, Paris, 1894, §§604, 605.
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  • [3] C. G. J. Jacobi, Zur Theorie der Variationsrechnung und der Differentialgleichungen, Werke, vol. 4.
  • [4] A. Hirsch, Über eine charakteristische Eigenschaft der Differentialgleichungen der Variationsrechnung, Mathematische Annalen, vol. 49 (1897), pp. 49-72.
  • [5] J. Kürschak, Über eine charakteristische Eigenschaft der Differentialgleichungen der Variationsrechnung, Mathematische Annalen, vol. 60 (1905), pp. 157-165. MR 1511292
  • [6] D. R. Davis, The inverse problem of the calculus of variations in higher space, these Transactions, vol. 30 (1928), pp. 710-736. MR 1501455
  • [7] D. R. Davis, The inverse problem of the calculus of variations in a space of $ (n + 1)$ dimensions, Bulletin of the American Mathematical Society, vol. 35 (1929), pp. 371-380. MR 1561747
  • [8] J. Douglas, Solution of the inverse problem of the calculus of variations, Proceedings of the National Academy of Sciences, vol. 25 (1939), pp. 631-637. MR 0000463 (1:78b)
  • [9] J. Douglas, Theorems in the inverse problem of the calculus of variations, ibid., vol. 26 (1940), pp. 215-221. MR 0001470 (1:244b)

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DOI: https://doi.org/10.1090/S0002-9947-1941-0004740-5
Article copyright: © Copyright 1941 American Mathematical Society

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