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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 506, Pages 20–24
DOI: https://doi.org/10.31857/S2686954322050046 (Mi danma291) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Applications of Zvonkin's transform to stationary Kolmogorov equations

V. I. Bogachevabc, M. Röcknerd, S. V. Shaposhnikovab

a Lomonosov Moscow State University
b HSE University, Moscow, Russia
c St. Tikhon's Orthodox University, Moscow, Russia
d Bielefeld University, Bielefeld, Germany
Citations (1)
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DOI: https://doi.org/10.31857/S2686954322050046
Abstract: In this note we develop a new analytic version of Zvonkin’s transform of the drift coefficient of a stationary Kolmogorov equation and apply this transform to derive the Harnack inequality for nonnegative solutions in the case where the diffusion matrix is not locally Sobolev. We also obtain a generalization of the known theorem of Hasminskii on existence of a probability solution to the stationary Kolmogorov equation.
Keywords: stationary Kolmogorov equation, Dini’s condition, class VMO, Zvonkin’s transform.
Funding agency Grant number
Russian Science Foundation 22-11-00015
Contest «Young Russian Mathematics»
This research is supported by the Russian Science Foundation, grant no. 22-11-00015. S.V. Shaposhnikov is a winner of the contest “Young Mathematics of Russia” and thanks its jury and sponsors.
Presented: A. N. Shiryaev
Received: 31.05.2022
Revised: 19.06.2022
Accepted: 15.07.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 2, Pages 318–321
DOI: https://doi.org/10.1134/S1064562422050064
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: V. I. Bogachev, M. Röckner, S. V. Shaposhnikov, “Applications of Zvonkin's transform to stationary Kolmogorov equations”, Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022), 20–24; Dokl. Math., 106:2 (2022), 318–321
Citation in format AMSBIB
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\by V.~I.~Bogachev, M.~R\"ockner, S.~V.~Shaposhnikov
\paper Applications of Zvonkin's transform to stationary Kolmogorov equations
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\vol 506
\pages 20--24
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\crossref{https://doi.org/10.31857/S2686954322050046}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4531977}
\elib{https://elibrary.ru/item.asp?id=49787595}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 2
\pages 318--321
\crossref{https://doi.org/10.1134/S1064562422050064}
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    • This publication is cited in the following 1 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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