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Calculus of variations with convexity constraint

Carlier, Guillaume (2002), Calculus of variations with convexity constraint, Journal of Nonlinear and Convex Analysis, 3, 2, p. 125-143

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Type
Article accepté pour publication ou publié
Date
2002
Journal name
Journal of Nonlinear and Convex Analysis
Volume
3
Number
2
Publisher
Yokohama Publishers
Pages
125-143
Metadata
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Author(s)
Carlier, Guillaume
Abstract (EN)
This article studies calculus of variations problems under a convexity constraint. The main motivations are Newton’s least resistance problem and mathematical economics. First a compactness result is proved which enables us to prove existence of solutions for nonconvex lagrangians or functionals with linear growth. Then a first order necessary condition is established by a penalization method. Finally, several examples of applications are derived from the latter.
Subjects / Keywords
calculus of variations problems