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.
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.
Accepted:
Published online:
Marc Quincampoix 1; Nadia Zlateva 1, 2
@article{CRMATH_2006__343_1_69_0,
author = {Marc Quincampoix and Nadia Zlateva},
title = {On {Lipschitz} regularity of minimizers of a calculus of variations problem with non locally bounded {Lagrangians}},
journal = {Comptes Rendus. Math\'ematique},
pages = {69--74},
publisher = {Elsevier},
volume = {343},
number = {1},
year = {2006},
doi = {10.1016/j.crma.2006.05.006},
language = {en},
}
TY - JOUR AU - Marc Quincampoix AU - Nadia Zlateva TI - On Lipschitz regularity of minimizers of a calculus of variations problem with non locally bounded Lagrangians JO - Comptes Rendus. Mathématique PY - 2006 SP - 69 EP - 74 VL - 343 IS - 1 PB - Elsevier DO - 10.1016/j.crma.2006.05.006 LA - en ID - CRMATH_2006__343_1_69_0 ER -
%0 Journal Article %A Marc Quincampoix %A Nadia Zlateva %T On Lipschitz regularity of minimizers of a calculus of variations problem with non locally bounded Lagrangians %J Comptes Rendus. Mathématique %D 2006 %P 69-74 %V 343 %N 1 %I Elsevier %R 10.1016/j.crma.2006.05.006 %G en %F CRMATH_2006__343_1_69_0
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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⁎ Work supported by the European Community's Human Potential Program HPRN-CT-2002-00281 [Evolution Equations].
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