%0 Journal Article
%T Contraction of general transportation costs along solutions to Fokker-Planck equations with monotone drifts
%A Luca Natile
%A Mark A. Peletier
%A Giuseppe Savar¨¦
%J Mathematics
%D 2010
%I arXiv
%X We shall prove new contraction properties of general transportation costs along nonnegative measure-valued solutions to Fokker-Planck equations in $R^d$, when the drift is a monotone (or $\lambda$-monotone) operator. A new duality approach to contraction estimates has been developed: it relies on the Kantorovich dual formulation of optimal transportation problems and on a variable-doubling technique. The latter is used to derive a new comparison property of solutions of the backward Kolmogorov (or dual) equation. The advantage of this technique is twofold: it directly applies to distributional solutions without requiring stronger regularity and it extends the Wasserstein theory of Fokker-Planck equations with gradient drift terms started by Jordan-Kinderlehrer-Otto (1998) to more general costs and monotone drifts, without requiring the drift to be a gradient and without assuming any growth conditions.
%U http://arxiv.org/abs/1002.0088v1