[Continuité hölderienne des solutions d'un problème de calcul des variations]
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.
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.
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@article{CRMATH_2008__346_23-24_1301_0,
author = {Pierre Bousquet and Carlo Mariconda and Giulia Treu},
title = {H\"older continuity of solutions to a basic problem in the calculus of variations},
journal = {Comptes Rendus. Math\'ematique},
pages = {1301--1305},
publisher = {Elsevier},
volume = {346},
number = {23-24},
year = {2008},
doi = {10.1016/j.crma.2008.10.001},
language = {en},
}
TY - JOUR AU - Pierre Bousquet AU - Carlo Mariconda AU - Giulia Treu TI - Hölder continuity of solutions to a basic problem in the calculus of variations JO - Comptes Rendus. Mathématique PY - 2008 SP - 1301 EP - 1305 VL - 346 IS - 23-24 PB - Elsevier DO - 10.1016/j.crma.2008.10.001 LA - en ID - CRMATH_2008__346_23-24_1301_0 ER -
%0 Journal Article %A Pierre Bousquet %A Carlo Mariconda %A Giulia Treu %T Hölder continuity of solutions to a basic problem in the calculus of variations %J Comptes Rendus. Mathématique %D 2008 %P 1301-1305 %V 346 %N 23-24 %I Elsevier %R 10.1016/j.crma.2008.10.001 %G en %F CRMATH_2008__346_23-24_1301_0
Pierre Bousquet; Carlo Mariconda; Giulia Treu. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.10.001/
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