Estimates of distances between solutions of Fokker–Planck–Kolmogorov equations with partially degenerate diffusion matrices

Using a metric which interpolates between the Kantorovich metric and the total variation norm we estimate the distance between solutions to Fokker–Planck–Kolmogorov equations with degenerate diffusion matrices. Some relations between the degeneracy of the diffusion matrix and the regularity of the drift coefficient are analysed. Applications to nonlinear Fokker–Planck–Kolmogorov equations are given.