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

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.

Presented at OTFUSA'2005, International Conference on "Operator Theory, Function Spaces and Applications", dedicated to the 60th birthday of Professor F.-O. Speck, 7-9 July 2005, Aveiro, Portugal