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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 5, Pages 141–148 (Mi izv2675)  

This article is cited in 8 scientific papers (total in 8 papers)

ACL and differentiability of a generalization of quasi-conformal maps

R. R. Salimov

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

Abstract: It is established that $Q$-homeomorphisms (in the sense of O. Martio) defined in $\mathbb{R}^n$, $n\geq2$, are absolutely continuous on lines. Furthermore, they belong to the Sobolev class $W_{\mathrm{loc}}^{1,1}$ and are differentiable almost everywhere for $Q\in L^{1}_{\mathrm{loc}}$.

DOI: https://doi.org/10.4213/im2675

Full text: PDF file (431 kB)
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English version:
Izvestiya: Mathematics, 2008, 72:5, 977–984

Bibliographic databases:

UDC: 517.5
MSC: 31B15, 30C65, 30C75, 30E25, 46E35
Received: 14.06.2007
Revised: 04.12.2007

Citation: R. R. Salimov, “ACL and differentiability of a generalization of quasi-conformal maps”, Izv. RAN. Ser. Mat., 72:5 (2008), 141–148; Izv. Math., 72:5 (2008), 977–984

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Salimov R.R., Sevost'yanov E.A., “Estimation of Dilatations for Mappings More General Than Quasiregular Mappings”, Ukr. Math. J., 62:11 (2011), 1775–1782  crossref  mathscinet  isi  scopus
    2. E. A. Sevost'yanov, “On the local behavior of mappings with unbounded quasiconformality coefficient”, Siberian Math. J., 53:3 (2012), 520–531  mathnet  crossref  mathscinet  isi
    3. R. R. Salimov, “On the Lipschitz Property of a Class of Mappings”, Math. Notes, 94:4 (2013), 559–566  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Cristea M., “On Generalized Quasiconformal Mappings”, Complex Var. Elliptic Equ., 59:2 (2014), 232–246  crossref  mathscinet  zmath  isi  scopus
    5. R. R. Salimov, “O koltsevykh $Q$-otobrazheniyakh otnositelno nekonformnogo modulya”, Dalnevost. matem. zhurn., 14:2 (2014), 257–269  mathnet
    6. R. R. Salimov, “Lower estimates of $p$-modulus and mappings of Sobolev's class”, St. Petersburg Math. J., 26:6 (2015), 965–984  mathnet  crossref  mathscinet  isi  elib  elib
    7. R. R. Salimov, “O konechnoi lipshitsevosti klassov Orlicha–Soboleva”, Vladikavk. matem. zhurn., 17:1 (2015), 64–77  mathnet
    8. V. A. Klyachin, N. A. Chebanenko, “O geometricheskikh svoistvakh nepreryvnykh otobrazhenii, sokhranyayuschikh orientatsiyu simpleksov”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:3 (2017), 294–303  mathnet  crossref  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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