Solutions for nonlinear Fokker–Planck equations with measures as initial data and McKean-Vlasov equations

One proves the existence and uniqueness of a generalized (mild) solution for nonlinear Fokker–Planck equation (FPE) u t ? ? ( ? ) + div D x b = 0 , ? ? R d ? 2 ? in where L 1 C is nondecreasing function, bounded, ? ; with strictly increasing, if not constant. Moreover, ? semigroup contractions which leaves invariant set probability density functions . If ? r | ? ? 3 then m > extends to initial data space M bounded measures As consequence arbitrary laws, we obtain weak solutions class McKean-Vlasov SDEs coefficients have singular dependence on time marginal laws.