[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 = {Bousquet, Pierre and Mariconda, Carlo and Treu, Giulia},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.10.001/}
}
TY - JOUR AU - Bousquet, Pierre AU - Mariconda, Carlo AU - Treu, Giulia 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2008.10.001/ DO - 10.1016/j.crma.2008.10.001 LA - en ID - CRMATH_2008__346_23-24_1301_0 ER -
%0 Journal Article %A Bousquet, Pierre %A Mariconda, Carlo %A Treu, Giulia %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 %U http://www.numdam.org/articles/10.1016/j.crma.2008.10.001/ %R 10.1016/j.crma.2008.10.001 %G en %F CRMATH_2008__346_23-24_1301_0
Bousquet, Pierre; Mariconda, Carlo; Treu, Giulia. Hölder continuity of solutions to a basic problem in the calculus of variations. Comptes Rendus. Mathématique, Tome 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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