Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Dokl. RAN. Math. Inf. Proc. Upr.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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
\Bibitem{BogRocSha22}
\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.
\yr 2022
\vol 506
\pages 20--24
\mathnet{http://mi.mathnet.ru/danma291}
\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}
Linking options:
  • https://www.mathnet.ru/eng/danma291
  • https://www.mathnet.ru/eng/danma/v506/p20
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
    Statistics & downloads:
    Abstract page:143
    References:23
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024