First integrals for problems of calculus of variations on locally convex spaces

• Author(s): Rocha, E.A.M. ; Torres, D.F.M.
• Date: 2008
• Persistent ID: http://hdl.handle.net/10773/4089
• Origin: RIA - Repositório Institucional da Universidade de Aveiro
• Subject(s): Calculus of variations; Locally convex spaces; Noether's theorem
• Document Type: Article
• Language: English

Description

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 Eulcr-Lagrange equations (Orlov. 2002) for continuously normally differentiable Lagrangians. Here, we formulate a Legcndre condition and an extension of the classical theorem of Emmy Noethcr, thus obtaining first integrals for problems of the calculus of variations on locally convex spaces. © Balkan Society of Geometers, Geometry Balkan Press 2008.