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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the definition and properties of certain variational integrals
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by James Serrin PDF
Trans. Amer. Math. Soc. 101 (1961), 139-167 Request permission
References
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    • C. B. Morrey, Multiple integral problems in the calculus of variations and related topics, Univ. California Publ. Math., 1943. Especially Chapter III. M. Nagumo, Über die gleichmässige Summierbarkeit und ihre Anwendung auf ein Variationsproblem, Jap. J. Math. vol. 6 (1929) pp. 173-182. See also L. M. Graves, The theory of functions of real variables, New York, McGraw-Hill, 1946, p. 235. C. Y. Pauc, La méthode métrique en calcul des variations, Paris, Hermann, 1941. Especially p. 54. S. Saks, Theory of the integral, 2d ed., Hafner, 1937.
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    • —, On the area of a surface $z = f(x,y)$, Amer. Math. Monthly vol. 68 (1961) pp. 435-440.
  • A. G. Sigalov, Two-dimensional problems of the calculus of variations in nonparametric form, Trudy Moskov. Mat. Obšč. 2 (1953), 201–233 (Russian). MR 0058884
    • L. Tonelli, Sulla quadratura delle superficie, Rend. Accad. Naz. Lincei (6) vol. 3 (1926) pp. 357-363, 445-450, 633-638.
  • Leonida Tonelli, Sur la semi-continuité des intégrales doubles du calcul des variations, Acta Math. 53 (1929), no. 1, 325–346 (French). MR 1555297, DOI 10.1007/BF02547573
    • I. Verchenko, Über das Flächenmass von Mengen, Mat. Sb. (N.S.) vol. 10 (1942) pp. 11-32.
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Additional Information
  • © Copyright 1961 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 101 (1961), 139-167
  • MSC: Primary 49.00
  • DOI: https://doi.org/10.1090/S0002-9947-1961-0138018-9
  • MathSciNet review: 0138018