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Regularity of solutions for some variational problems subject to a convexity constraint
Author(s) -
Carlier G.,
LachandRobert T.
Publication year - 2001
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3
Subject(s) - convexity , mathematics , constraint (computer aided design) , boundary (topology) , class (philosophy) , regular polygon , boundary value problem , convex function , dirichlet boundary condition , dirichlet distribution , calculus of variations , mathematical analysis , dirichlet problem , subject (documents) , pure mathematics , geometry , computer science , artificial intelligence , financial economics , economics , library science
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.