Proper extensions of Noether's symmetry theorem for nonsmooth extremals of the calculus of variations

Communications on Pure and Applied Analysis

Volumn 3, Issue 3, 2004, Pages 491-500

  Torres, Delfim F M ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Calculus of variations; DuBois Reymond extremals; Euler Lagrange extremals; Higher order variational problems; Lipschitz admissible functions; Noether's theorem

Indexed keywords

EID: 24944485940     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2004.3.491     Document Type: Article

References (12)

1. V.M. Alekseev, V.M. Tikhomirov and S.V. Fomin, "Optimal Control", Consultants Bureau, New York, 1987.
2. L. Cesari, "Optimization-Theory and Applications", Springer-Verlag, New York, 1983.
3. F.H. Clarke, "Methods of Dynamic and Nonsmooth Optimization", Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1989.
4. I.M. Gelfand and S.V. Fomin, "Calculus of Variations", Dover Publications, Mineola, NY, 2000.
5. M. Giaquinta and S. Hildebrandt, "Calculus of Variations I-The Lagrangian Formalism", Springer-Verlag, Berlin, 1996.
6. J. Jost and X. Li-Jost, "Calculus of Variations", Cambridge University Press, Cambridge, 1998.
7. S. Moyo and P.G.L. Leach, A Note on the Construction of the Ermakov-Lewis Invariant, J. Phys. A: Math. Gen., 35 (2002), 5333-5345.
8. E. Noether, Invariante Variationsprobleme, Gött. Nachr., (1918), 235-257.
9. E. Noether, Invariant Variation Problems, Transport Theory Statist. Phys., (3) 1 (1971), 186-207. English translation of the original paper [8].
10. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, "The Mathematical Theory of Optimal Processes", Interscience Publishers John Wiley & Sons, Inc. New York-London, 1962.
11. W. Sarlet and F. Cantrijn, Generalizations of Noether's Theorem in Classical Mechanics, SIAM Rev., (4) 23 (1981), 467-494.
12. D.F.M. Torres, On the Noether Theorem for Optimal Control, European Journal of Control, (1) 8 (2002), 56-63.