Estimates for Kantorovich functionals between solutions to Fokker -- Planck -- Kolmogorov equations with dissipative drifts

Abstract

We obtain estimates for the Kantorovich functionals between solutions to different Fokker -- Planck -- Kolmogorov equations for measures with same diffusion part but different drifts and different initial conditions. We show possible applications of such estimates to the study of the well-posedness for nonlinear equations.