Quantitative stability estimates for Fokker-Planck equations

Abstract: We consider the Fokker--Planck equations with irregular coefficients. Two different cases are treated: in the degenerate case, the coefficients are assumed to be weakly differentiable, while in the non-degenerate case the drift satisfies only the Ladyzhenskaya--Prodi--Serrin condition. Using Trevisan's superposition principle which represents the solution as the marginal of the solution to the martingale problem of the diffusion operator, we establish quantitative stability estimates for the solutions of Fokker--Planck equations.