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A Lipschitz regularity theorem

Published online by Cambridge University Press:  01 December 2007

FRANCIS CLARKE
FRANCIS CLARKE*
Affiliation:
Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France (email: [email protected])
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Abstract

This paper gives a direct and elementary proof of the fact that under hypotheses of Tonelli type, solutions to the basic problem in the calculus of variations are Lipschitz when the Lagrangian is autonomous. This fact was first proved by Clarke and Vinter in 1985, using other methods.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 6 , December 2007 , pp. 1713 - 1718
Copyright
Copyright © Cambridge University Press 2007

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References

[1]Clarke, F.. Necessary conditions in dynamic optimization. Mem. Amer. Math. Soc. 173(816) (2005).Google Scholar
[2]Clarke, F. H. and Vinter, R. B.. On the conditions under which the Euler equation or the maximum principle hold. Appl. Math. Optim. 12 (1984), 73–79.CrossRefGoogle Scholar
[3]Clarke, F. H. and Vinter, R. B.. Regularity properties of solutions to the basic problem in the calculus of variations. Trans. Amer. Math. Soc. 289 (1985), 73–98.CrossRefGoogle Scholar
[4]Vinter, R. B.. Optimal Control. Birkhäuser, Boston, MA, 2000.Google Scholar