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 Sibirsk. Mat. Zh., 2009, Volume 50, Number 3, Pages 526–546 (Mi smj1979)

Stability of mappings with bounded distortion in the Sobolev norm on the John domains of Heisenberg groups

D. V. Isangulova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: This article completes the authors's series on stability in the Liouville theorem on the Heisenberg group. We show that every mapping with bounded distortion on a John domain of the Heisenberg group is approximated by a conformal mapping with order of closeness $\sqrt{K-1}$ in the uniform norm and with order of closeness $K-1$ in the Sobolev $L^1_p$-norm for all $p<\frac C{K-1}$. We construct two examples, demonstrating the asymptotic sharpness of our results.

Keywords: Heisenberg group, mapping with bounded distortion, John domain, Möbius transformation.

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English version:
Siberian Mathematical Journal, 2009, 50:3, 415–433

Bibliographic databases:

UDC: 517.54

Citation: D. V. Isangulova, “Stability of mappings with bounded distortion in the Sobolev norm on the John domains of Heisenberg groups”, Sibirsk. Mat. Zh., 50:3 (2009), 526–546; Siberian Math. J., 50:3 (2009), 415–433

Citation in format AMSBIB
\Bibitem{Isa09} \by D.~V.~Isangulova \paper Stability of mappings with bounded distortion in the Sobolev norm on the John domains of Heisenberg groups \jour Sibirsk. Mat. Zh. \yr 2009 \vol 50 \issue 3 \pages 526--546 \mathnet{http://mi.mathnet.ru/smj1979} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2555879} \elib{http://elibrary.ru/item.asp?id=12941118} \transl \jour Siberian Math. J. \yr 2009 \vol 50 \issue 3 \pages 415--433 \crossref{https://doi.org/10.1007/s11202-009-0048-x} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000266951900005} \elib{http://elibrary.ru/item.asp?id=13616056} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67650482371} 

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