Regularity of solutions for some variational problems subject to a convexity constraint
Lachand-Robert, Thomas; Carlier, Guillaume (2001), Regularity of solutions for some variational problems subject to a convexity constraint, Communications on Pure and Applied Mathematics, 54, 5, p. 583-594. http://dx.doi.org/10.1002/cpa.3
TypeArticle accepté pour publication ou publié
Journal nameCommunications on Pure and Applied Mathematics
MetadataShow full item record
Abstract (EN)We first study the minimizers, in the class of convex functions, of an elliptic functional with nonhomogeneous Dirichlet boundary conditions. We prove C1 regularity of the minimizers under the assumption that the upper envelope of admissible functions is C1. This condition is optimal at least when the functional depends only on the gradient . We then give various extensions of this result. In Particular, we consider a problem without boundary conditions arising in an economic model introduced by Rochet and Choné in .
Subjects / KeywordsConvexity constraint; Calcul variationnel; Variational calculus; Fonctions convexes
Showing items related by title and author.