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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Silverman necessary condition for multiple integrals in the calculus of variations


Author: J. Ernest Wilkins
Journal: Proc. Amer. Math. Soc. 44 (1974), 409-410
MSC: Primary 49B20
DOI: https://doi.org/10.1090/S0002-9939-1974-0350572-5
MathSciNet review: 0350572
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Abstract: A necessary condition for a weak relative minimum of a multiple integral in the calculus of variations, recently derived by Silverman, is shown to be a consequence of (and hence equivalent to) the well-known Legendre-Hadamard necessary condition in the special cases of a double, triple or quadruple integral.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0350572-5
Keywords: Legendre-Hadamard necessary condition
Article copyright: © Copyright 1974 American Mathematical Society