Regularity of solutions for some variational problems subject to a convexity constraint

Lachand-Robert, Thomas; Carlier, Guillaume

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

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Type

Article accepté pour publication ou publié

Date

2001

Journal name

Communications on Pure and Applied Mathematics

Volume

Number

Publisher

John Wiley & Sons, Inc.

Pages

583-594

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 [3]. 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 [4].

Subjects / Keywords

Convexity constraint; Calcul variationnel; Variational calculus; Fonctions convexes