A nonintersection property for extremals of variational problems with vector-valued functions
type: Item
instance of: scholarly article
title: A nonintersection property for extremals of variational problems with vector-valued functions
zbMATH Open document ID: 1208.49023
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2007-03-29T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78721
review text: The author considers the classical problem of calculus of variations, i.e., the one of minimizing the integral of some Lagrangian function over a function whose end-point values are fixed (the function of time to be minimized has value in an Euclidean space). He studies the class of functions of time which are bounded and solution of these problems of calculus of variations for any initial and final time, with of course compatible end-point conditions. His main results are that (i) if such a function has the same value at two different times, then it is periodic, (ii) if two such functions have the same value at given times, then they coincide (perhaps up to a translation).
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49N20
zbMATH DE Number: 5138727
zbMATH Keywords: calculus of variations
zbMATH Keywords: variational problems
zbMATH Keywords: periodic extremal
zbMATH Keywords: good functions
author: Alexander J. Zaslavski
reviewed by: J. Frédéric Bonnans
MaRDI profile type: Publication
OpenAlex ID: W1994156623
cites work: Q3814339
cites work: On minimal laminations of the torus
cites work: Q4743352
cites work: On the regularity of the minima of variational integrals
cites work: Geodesics on a two-dimensional Riemannian manifold with periodic coefficients
cites work: Infinite horizon autonomous systems with unbounded cost
cites work: One-dimensional infinite-horizon variational problems arising in continuum mechanics
cites work: The structure of extremals of a class of second order variational problems
cites work: The structure and limiting behavior of locally optimal minimizers.
cites work: Minimal solutions of variational problems on a torus
cites work: On some results of Moser and of Bangert
cites work: On Some Results of Moser and of Bangert, II
cites work: The existence of periodic minimal energy configurations for one-dimensional infinite horizon variational problems arising in continuum mechanics
cites work: Dynamic properties of optimal solutions of variational problems
cites work: Existence and uniform boundedness of optimal solutions of variational problems
cites work: The turnpike property for extremals of nonautonomous variational problems with vector-valued functions
cites work: Q5480080
cites work: Turnpike properties in the calculus of variations and optimal control
DOI: 10.1016/J.ANIHPC.2006.01.002
description: scientific article; zbMATH DE number 5138727