Abstract

Using a result of Y. Brenier [Comm. Pure Appl. Math. 44 (1991) 375--417] we give a representation of the polar cone of monotone gradient fields in terms of measure-preserving maps, or bistochastic measures. Some applications to variational problems subject to a convexity constraint are given.

Author information

Contact details are reproduced from the original publication and may be historical.

Thomas Lachand-Robert

Lab. de Mathématiques, Université de Savoie, 73376 Le Bourget-du-Lac, France

Keywords

  • Convexity constraint
  • Euler-Lagrange equation
  • measure-preserving maps
  • bistochastic measures

Suggested citation

G. Carlier, T. Lachand-Robert. “Representation of the Polar Cone of Convex Functions and Applications.” Journal of Convex Analysis 15 (2008), No. 3, 535–546.

Copyright Heldermann Verlag 2008