Holder continuity of solutions to a basic problem in the calculus of variations

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 phi. When phi is Lipschitz continuous, then the Solutions are Holder continuous. To cite this article: P. Bousquet et al., C R. Acad. Sci. Paris, Ser. I 346 (2008). (C) 2008 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.