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Tr. Mosk. Mat. Obs., 2013, Volume 74, Issue 1, Pages 17–34 (Mi mmo539)  

This article is cited in 3 scientific papers (total in 3 papers)

The Fokker–Planck–Kolmogorov equations with a potential and a non-uniformly elliptic diffusion matrix

S. V. Shaposhnikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We study solutions of the Fokker–Planck–Kolmogorov equation with unbounded coefficients and a non-uniformly elliptic diffusion matrix. Upper bounds for solutions are obtained. In addition, new estimates with a Lyapunov function are obtained.

Key words and phrases: parabolic equations for measures; Fokker–Planck–Kolmogorov equation; diffusion processes.

Full text: PDF file (301 kB)
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English version:
Transactions of the Moscow Mathematical Society, 2013, 74, 15–29

Bibliographic databases:

UDC: 517.986.7
MSC: 35R15, 35K10, 60J60
Received: 05.02.2013

Citation: S. V. Shaposhnikov, “The Fokker–Planck–Kolmogorov equations with a potential and a non-uniformly elliptic diffusion matrix”, Tr. Mosk. Mat. Obs., 74, no. 1, MCCME, M., 2013, 17–34; Trans. Moscow Math. Soc., 74 (2013), 15–29

Citation in format AMSBIB
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\by S.~V.~Shaposhnikov
\paper The Fokker--Planck--Kolmogorov equations with a potential and a non-uniformly elliptic diffusion matrix
\serial Tr. Mosk. Mat. Obs.
\yr 2013
\vol 74
\issue 1
\pages 17--34
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo539}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3123622}
\zmath{https://zbmath.org/?q=an:06371554}
\elib{http://elibrary.ru/item.asp?id=21369362}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2013
\vol 74
\pages 15--29
\crossref{https://doi.org/10.1090/S0077-1554-2014-00211-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84945127497}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Manita O.A., Romanov M.S., Shaposhnikov S.V., “on Uniqueness of Solutions To Nonlinear Fokker-Planek-Kolmogorov Equations”, Nonlinear Anal.-Theory Methods Appl., 128 (2015), 199–226  crossref  mathscinet  zmath  isi  scopus
    2. M. Kunze, L. Lorenzi, A. Rhandi, “Kernel estimates for nonautonomous Kolmogorov equations”, Adv. Math., 287 (2016), 600–639  crossref  mathscinet  zmath  isi  elib  scopus
    3. V. I. Bogachev, M. Roeckner, S. V. Shaposhnikov, “Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations”, J. Funct. Anal., 271:5 (2016), 1262–1300  crossref  mathscinet  zmath  isi  scopus
  • Trudy Moskovskogo Matematicheskogo Obshchestva
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