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
TypeArticle accepté pour publication ou publié
Journal nameJournal of Nonlinear and Convex Analysis
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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 / Keywordscalculus of variations problems
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