Nonlinear Fokker–Planck–Kolmogorov Equations for Measures

  • Stanislav V. ShaposhnikovEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)


Existence and uniqueness of solutions of the Cauchy problem for nonlinear Fokker–Planck–Kolmogorov equations for measures are investigated. We consider the difficult case when the diffusion matrix depends on the solution. Moreover we give a short survey of the known results connected with these problems.


Nonlinear Fokker–Planck–Kolmogorov equation McKean–Vlasov equation Existence and uniqueness of solutions to the Cauchy problem for nonlinear parabolic equations 

AMS subject classification.

35K55 35Q84 35Q83 



The author is grateful to Prof. V.I. Bogachev and Prof. M. Röckner for fruitful discussions and valuable remarks. The work was supported by the President Grant MD-207.2017.1, the RFBR grant 17-01-00622, the Simons Foundation, and the SFB 1283 at Bielefeld University.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.St.-Tikhon’s Orthodox Humanitarian UniversityMoscowRussia

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