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

✍ Scribed by G. Carlier; T. Lachand-Robert

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 76 KB
Volume: 54
Category: Article
ISSN: 0010-3640
DOI: 10.1002/cpa.3

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✦ Synopsis

Abstract

We first study the minimizers, in the class of convex functions, of an elliptic functional with nonhomogeneous Dirichlet boundary conditions. We prove C^1^ regularity of the minimizers under the assumption that the upper envelope of admissible functions is C^1^. 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]. © 2001 John Wiley & Sons, Inc.

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