Sibirskii Matematicheskii Zhurnal
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



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Sibirskii Matematicheskii Zhurnal, 2007, Volume 48, Number 2, Pages 313–334 (Mi smj25)  

This article is cited in 13 scientific papers (total in 13 papers)

The class of mappings with bounded specific oscillation, and integrability of mappings with bounded distortion on Carnot groups

D. V. Isangulova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
References:
Abstract: This paper is the first of the author's three articles on stability in the Liouville theorem on the Heisenberg group. The aim is to prove that each mapping with bounded distortion of a John domain on the Heisenberg group is close to a conformal mapping with order of closeness $\sqrt{K-1}$ in the uniform norm and order of closeness $K-1$ in the Sobolev norm $L_p^1$ for all $p<\frac C{K-1}$.
In the present article we study integrability of mappings with bounded specific oscillation on spaces of homogeneous type. As an example, we consider mappings with bounded distortion on the Heisenberg group. We prove that a mapping with bounded distortion belongs to the Sobolev class $W^1_{p,\mathrm{loc}}$, where $p\to\infty$ as the distortion coefficient tends to 1.
Keywords: space of homogeneous type, mapping with bounded specific oscillation, Carnot group, Heisenberg group, mapping with bounded distortion.
Received: 11.10.2005
English version:
Siberian Mathematical Journal, 2007, Volume 48, Issue 2, Pages 249–267
DOI: https://doi.org/10.1007/s11202-007-0025-1
Bibliographic databases:
UDC: 517.54
Language: Russian
Citation: D. V. Isangulova, “The class of mappings with bounded specific oscillation, and integrability of mappings with bounded distortion on Carnot groups”, Sibirsk. Mat. Zh., 48:2 (2007), 313–334; Siberian Math. J., 48:2 (2007), 249–267
Citation in format AMSBIB
\Bibitem{Isa07}
\by D.~V.~Isangulova
\paper The class of mappings with bounded specific oscillation, and integrability of mappings with bounded distortion on Carnot groups
\jour Sibirsk. Mat. Zh.
\yr 2007
\vol 48
\issue 2
\pages 313--334
\mathnet{http://mi.mathnet.ru/smj25}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2330061}
\zmath{https://zbmath.org/?q=an:1164.30362}
\transl
\jour Siberian Math. J.
\yr 2007
\vol 48
\issue 2
\pages 249--267
\crossref{https://doi.org/10.1007/s11202-007-0025-1}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000245965600005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34147191577}
Linking options:
  • https://www.mathnet.ru/eng/smj25
  • https://www.mathnet.ru/eng/smj/v48/i2/p313
  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
    Statistics & downloads:
    Abstract page:466
    Full-text PDF :124
    References:74
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024