[Mini Courses] Nonlinear Fokker-Planck equations (of Nemytskii-type) and their applications to McKean-Vlasov equations I

• The lectures consist of three parts: (a) Existence of mild and weak solutions to Fokker-Planck equations of (Nemytskii-type); (b) Uniqueness of weak solutions; (c) Applications to McKean-Vlasov (also called distribution dependent) stochastic differential equations. In addition to the formulation and explanation of the results, also the main ideas as well as key parts of the proofs will be presented in some detail. The contents of all three parts of the lectures is taken from the following three papers coauthored by Viorel Barbu from the Romanian Academy of Sciences in Iasi and will be the core of a joint monograph which is in preparation.

• Barbu, Viorel; Röckner, Michael, From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE. Ann. Probab. 48 (2020), no. 4, 1902–1920.

• Barbu, Viorel; Röckner, Michael, Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations. J. Funct. Anal. 280 (2021), no. 7, Paper No. 108926, 35 pp.

• Barbu, Viorel; Röckner, Michael, Uniqueness for nonlinear Fokker-Planck equations and for McKean-Vlasov SDEs: The degenerate case. arXiv:2203.00122.