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Comptes Rendus Mathématique
Volume 343, n° 1
pages 69-74 (juillet 2006)
Doi : 10.1016/j.crma.2006.05.006
Received : 25 May 2005 ;  accepted : 2 May 2006
On Lipschitz regularity of minimizers of a calculus of variations problem with non locally bounded Lagrangians
Sur la régularité lipschitzienne des solutions dʼun problème de calcul des variations avec lagrangiens non localement bornés
 

Marc Quincampoix a , Nadia Zlateva a, b
a Laboratoire de mathématiques, UMR CNRS 6205, 6, avenue Victor-le-Gorgeu, B.P. 809, 29285 Brest cedex, France 
b Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria 

Abstract

We prove that the optimal solutions of a calculus of variations problem are Lipschitz continuous. The result is obtained without assuming that the domain of the Lagrangian is the whole space as usually stated in the literature. So, the contribution of this Note is in giving a new sufficient condition for the nonexistence of a Lavrentiev phenomenon. To cite this article: M. Quincampoix, N. Zlateva, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
Résumé

Dans cette Note, nous prouvons que les solutions optimales dʼun problème de calcul des variations sont lipschitziennes. Ce résultat est obtenu sans supposer, comme souvent dans la littérature, que le lagrangien est défini sur tout lʼespace. Cet article donne donc une nouvelle condition suffisante pour lʼabsence de phénomène de Lavrentieff. Pour citer cet article : M. Quincampoix, N. Zlateva, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.

 Work supported by the European Communityʼs Human Potential Program HPRN-CT-2002-00281 [Evolution Equations].



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