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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.
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Oxana A. Manita, Estimates for transportation costs along solutions to Fokker–Planck–Kolmogorov equations with dissipative drifts. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 3, pp. 601–618DOI 10.4171/RLM/778