Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Hamiltonian analysis of the generalized problem of Bolza

Author: F. H. Clarke
Journal: Trans. Amer. Math. Soc. 301 (1987), 385-400
MSC: Primary 49B05; Secondary 58E30
MathSciNet review: 879580
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: On étudie le problème généralisé de Bolza en calcul des variations. Presented at the International Conference on the Calculus of Variations held to honour the memory of Leonida Tonelli, Scuola Normale Superiore, Pisa, March 1986. On obtient des conditions nécessaires en forme hamiltonienne, sous des hypothèses moins exigeantes qu'antérieurement, en particulier sans qualification sur les contraintes. Le lien avec les problèmes de contrôle optimal est développé, ainsi que l'apport de ces conditions à la théorie de la régularité de la solution.

We obtain necessary conditions in Hamiltonian form for the generalized problem of Bolza in the calculus of variations. These are proven in part by an extension to Hamiltonians of Tonelli's method of auxiliary Lagrangians. One version of the conditions is of a new character since it is obtained in the absence of any constraint qualification on the data. A new regularity theorem is shown to be a consequence of the necessary conditions.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 49B05, 58E30

Retrieve articles in all journals with MSC: 49B05, 58E30

Additional Information

PII: S 0002-9947(1987)0879580-6
Keywords: Bolza problem, calculus of variations, Hamiltonian, necessary conditions, nonsmooth analysis, generalized gradients, regularity
Article copyright: © Copyright 1987 American Mathematical Society