| Abstract: |
| To characterize the regularity of nonlinear Fokker-Planck equations with respect to weighted variational distances, we establish for the first time a Bismut type formula for the extrinsic derivative of distribution dependent SDEs (DDSDEs). As an application, the Lipschitz continuity in the weighted variational distance is derived for the associated nonlinear Fokker-Planck equation, which can be regarded as the counterpart of the classical contraction property in the linear setting. The main results are illustrated by non-degenerate DDSDEs with space-time singular drift, as well as degenerate DDSDEs with weakly monotone coefficients. |
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