Calculus of Variations
Hölder continuity of solutions to a basic problem in the calculus of variations
Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1301-1305.

For the basic problem in the calculus of variations where the Lagrangian is convex and depends only on the gradient, we establish the continuity of the solutions when the Dirichlet boundary condition is defined by a continuous function ϕ. When ϕ is Lipschitz continuous, then the solutions are Hölder continuous.

Pour un problème de calcul des variations multidimensionnel, où le lagrangien convexe ne dépend que du gradient, on montre que la continuité de la fonction ϕ définissant la condition de Dirichlet au bord implique la continuité des minimiseurs sur l'adhérence du domaine. Lorsque ϕ est lipschitzienne, alors les minimiseurs sont hölderiens.

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DOI: 10.1016/j.crma.2008.10.001
Bousquet, Pierre 1; Mariconda, Carlo 2; Treu, Giulia 2

1 UMPA, ENS Lyon, 46 Allée d'Italie, 69007 Lyon, France
2 Dipartimento di Matematica Pura e Applicata, Via Trieste 63, 35121 Padova, Italy
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Bousquet, Pierre; Mariconda, Carlo; Treu, Giulia. Hölder continuity of solutions to a basic problem in the calculus of variations. Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1301-1305. doi : 10.1016/j.crma.2008.10.001. http://www.numdam.org/articles/10.1016/j.crma.2008.10.001/

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