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Transactions of the American Mathematical Society

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Field theories in the modern calculus of variations

Author: Andrzej Nowakowski
Journal: Trans. Amer. Math. Soc. 309 (1988), 725-752
MSC: Primary 49B36; Secondary 49F22
MathSciNet review: 961610
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Abstract: Two methods of construction of fields of extremals ("geodesic coverings") in the generalized problem of Bolza are given and, as a consequence, sufficient conditions for optimality in a form similar to Weierstrass' are formulated. The first field theory is an extension of Young's field theory-- "concourse of flights" for our problem; the other describes a nonclassical treatment of field theory which allows one to reject the "self-multiplier restriction".

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Keywords: Sufficient conditions, strong relative minimality, generalized problem of Bolza, calculus of variations, field of extremals, self-multiplier restriction
Article copyright: © Copyright 1988 American Mathematical Society

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