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First Integrals for Problems of Calculus of Variations on Locally Convex Spaces

Eugenio A. M. Rocha·Delfim F. M. Torres
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Abstract

The fundamental problem of calculus of variations is considered when solutions are differentiable curves on locally convex spaces. Such problems admit an extension of the Euler-Lagrange equations [Orlov 2002] for continuously normally differentiable Lagrangians. Here, we formulate a Legendre condition and an extension of the classical theorem of Emmy Noether, thus obtaining first integrals for problems of the calculus of variations on locally convex spaces.

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Eugenio A. M. Rocha, Delfim F. M. Torres. 2005-11-14. First Integrals for Problems of Calculus of Variations on Locally Convex Spaces. https://arxiv.org/abs/math/0511347

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