Inserted: 30 dec 2005
Last Updated: 14 jan 2009
Journal: J. Glob. Opt.
After presenting an overview about variational problems on probability measures for functionals involving transport costs and extra terms encouraging or discouraging concentration, we look for optimality conditions, regularity properties and explicit computations in the case where Wasserstein distances and interaction energies are considered.
Keywords: regularity, Mass transportation, Monge-Ampère equation, interaction energy