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Journal of Mathematical Sciences

, Volume 207, Issue 2, pp 147–165 | Cite as

Uniqueness Problems for Degenerate Fokker–Planck–Kolmogorov Equations

  • V. I. BogachevEmail author
  • M. Röckner
  • S. V. Shaposhnikov
Article

We study the uniqueness of solutions to the Cauchy problem for the Fokker–Planck–Kolmogorov equation with a singular diffusion matrix in the class of probability measures. A survey of known result and methods is given. In addition, we obtain new sufficient conditions for the uniqueness in the case of unbounded coefficients and a partially singular diffusion matrix and also in the case where the diffusion matrix is a squared Lipschitzian matrix.

Keywords

Probability Measure Cauchy Problem Lebesgue Measure Borel Measure Planck Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • V. I. Bogachev
    • 1
    • 2
    Email author
  • M. Röckner
    • 3
  • S. V. Shaposhnikov
    • 1
    • 2
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.St. Tikhon’s Orthodox Humanitarian UniversityMoscowRussia
  3. 3.Universität BielefeldBielefeldGermany

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