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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A necessary condition in the calculus of variations


Author: Edward Silverman
Journal: Proc. Amer. Math. Soc. 37 (1973), 462-464
MSC: Primary 49B25
MathSciNet review: 0319009
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Abstract | References | Similar Articles | Additional Information

Abstract: A necessary condition that an extremal be a relative minimum is derived. The condition includes and may be stronger than the Legendre-Hadamard condition.


References [Enhancements On Off] (What's this?)

  • [1] J. Hadamard, Leçons sur la propagation des ondes et les équations de l'hydrodynamique, Hermann, Paris, 1903.
  • [2] Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. MR 0202511 (34 #2380)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0319009-5
PII: S 0002-9939(1973)0319009-5
Keywords: Legendre-Hadamard necessary condition, quasi-convex
Article copyright: © Copyright 1973 American Mathematical Society