A generalized notion of boundary
HTML articles powered by AMS MathViewer
- by W. H. Fleming and L. C. Young PDF
- Trans. Amer. Math. Soc. 76 (1954), 457-484 Request permission
References
-
P. Alexandroff and H. Hopf, Topologie, Berlin, 1935.
S. Banach, Théorie des opérations linéaires, Warsaw, 1932.
- Lamberto Cesari, An existence theorem of calculus of variations for integrals on parametric surfaces, Amer. J. Math. 74 (1952), 265–295. MR 50187, DOI 10.2307/2371993
- Wilhelm Damköhler, Über indefinite Variationsprobleme, Math. Ann. 110 (1935), no. 1, 230–283 (German). MR 1512938, DOI 10.1007/BF01448027
- Wilhelm Damköhler and Eberhard Hopf, Über einige Eigenschaften von Kurvenintegralen und über die Äquivalenz von indefiniten mit definiten Variationsproblemen, Math. Ann. 120 (1947), 12–20 (German). MR 22660, DOI 10.1007/BF01447822
- John M. Danskin Jr., On the existence of minimizing surfaces in parametric double integral problems of the calculus of variations, Riv. Mat. Univ. Parma 3 (1952), 43–63. MR 50186
- W. V. D. Hodge, The theory and applications of harmonic integrals, Cambridge, at the University Press, 1952. 2d ed. MR 0051571
- M. Krein and D. Milman, On extreme points of regular convex sets, Studia Math. 9 (1940), 133–138 (English, with Ukrainian summary). MR 4990, DOI 10.4064/sm-9-1-133-138
- Solomon Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications, Vol. 27, American Mathematical Society, New York, 1942. MR 0007093
- E. J. McShane, Generalized curves, Duke Math. J. 6 (1940), 513–536. MR 2469
- D. Mil′man, Characteristics of extremal points of regularly convex sets, Doklady Akad. Nauk SSSR (N.S.) 57 (1947), 119–122 (Russian). MR 0022313 S. Saks, Theory of the integral, Warsaw, 1937.
- A. G. Sigalov, Two-dimensional problems of the calculus of variations, Uspehi Matem. Nauk (N.S.) 6 (1951), no. 2(42), 16–101 (Russian). MR 0043400 L. C. Young, Generalized curves and the existence of an attained absolute minimum in the calculus of variations, Comptes Rendus de la Société des Sciences et des Lettres de Varsovie, Classe III, vol. 30 (1937) pp. 212-234.
- L. C. Young, Generalized surfaces in the calculus of variations, Ann. of Math. (2) 43 (1942), 84–103. MR 6023, DOI 10.2307/1968882
- L. C. Young, Generalized surfaces in the calculus of variations. II, Ann. of Math. (2) 43 (1942), 530–544. MR 6832, DOI 10.2307/1968809
- L. C. Young, Some applications of the Dirichlet integral to the theory of surfaces, Trans. Amer. Math. Soc. 64 (1948), 317–335. MR 26118, DOI 10.1090/S0002-9947-1948-0026118-7 —, Surfaces paramétriques généralisées, Bull. Soc. Math. France vol. 79 (1951) pp. 59-85.
Additional Information
- © Copyright 1954 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 76 (1954), 457-484
- MSC: Primary 49.0X
- DOI: https://doi.org/10.1090/S0002-9947-1954-0067377-7
- MathSciNet review: 0067377