Comptes Rendus
no. 1
Calculus of Variations
On Lipschitz regularity of minimizers of a calculus of variations problem with non locally bounded Lagrangians
[Sur la régularité lipschitzienne des solutions d'un problème de calcul des variations avec lagrangiens non localement bornés]

Présenté par : Alain Bensoussan

Marc Quincampoix1 ; Nadia Zlateva1, 2
1 Laboratoire de mathématiques, UMR CNRS 6205, 6, avenue Victor-le-Gorgeu, B.P. 809, 29285 Brest cedex, France
2 Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria
Comptes Rendus. Mathématique, Volume 343 (2006) no. 1, pp. 69-74.

Dans cette Note, nous prouvons que les solutions optimales d'un 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 l'espace. Cet article donne donc une nouvelle condition suffisante pour l'absence de phénomène de Lavrentieff.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.05.006
Marc Quincampoix 1 ; Nadia Zlateva 1, 2

1 Laboratoire de mathématiques, UMR CNRS 6205, 6, avenue Victor-le-Gorgeu, B.P. 809, 29285 Brest cedex, France
2 Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria 
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Marc Quincampoix; Nadia Zlateva. On Lipschitz regularity of minimizers of a calculus of variations problem with non locally bounded Lagrangians. Comptes Rendus. Mathématique, Volume 343 (2006) no. 1, pp. 69-74. doi : 10.1016/j.crma.2006.05.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.05.006/

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Cité par Sources :

⁎ Work supported by the European Community's Human Potential Program HPRN-CT-2002-00281 [Evolution Equations].

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