In this talk we shall ﬁrst review our recent results about the equivalence of non-linear Fokker-Planck equations and McKean Vlasov SDEs. Then we shall recall our results on existence of weak solutions to both such equations in the singular case, where the measure dependence of the coefﬁcients are of Nemytskii-type. The main new results to be presented are about weak uniqueness of solutions to both nonlinear Fokker-Planck equations and the corresponding McKean-Vlasov SDEs in the case of (possibly) degenerate diffusion coefﬁcients . As a consequence of this and one obtains that the laws on path space of the solutions to the McKean-Vlasov SDEs form a nonlinear Markov process in the sense of McKean.
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