Estimates for transportation costs along solutions to Fokker–Planck–Kolmogorov equations with dissipative drifts

Abstract

We obtain estimates for the Kantorovich transportation costs along solutions to different Fokker–Planck–Kolmogorov equations for measures with the same diffusion part but with different drifts and different initial conditions. We give applications of such estimates to the study of the well-posedness for nonlinear equations.