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Proceedings of the American Mathematical Society

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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: 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

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Keywords: Legendre-Hadamard necessary condition, quasi-convex
Article copyright: © Copyright 1973 American Mathematical Society