Abstract:
It is established that Q-homeomorphisms (in the sense of O. Martio) defined in Rn, n⩾2, are absolutely continuous on lines. Furthermore, they belong to the Sobolev class W1,1loc and are differentiable almost everywhere for Q∈L1loc.
\Bibitem{Sal08}
\by R.~R.~Salimov
\paper ACL and differentiability of a generalization of quasi-conformal maps
\jour Izv. Math.
\yr 2008
\vol 72
\issue 5
\pages 977--984
\mathnet{http://mi.mathnet.ru/eng/im2675}
\crossref{https://doi.org/10.1070/IM2008v072n05ABEH002425}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2473774}
\zmath{https://zbmath.org/?q=an:1175.31006}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2008IzMat..72..977S}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000261096200004}
\elib{https://elibrary.ru/item.asp?id=20358653}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-56849127154}
Linking options:
https://www.mathnet.ru/eng/im2675
https://doi.org/10.1070/IM2008v072n05ABEH002425
https://www.mathnet.ru/eng/im/v72/i5/p141
This publication is cited in the following 30 articles:
Ruslan Salimov, Bogdan Klishchuk, Trends in Mathematics, New Tools in Mathematical Analysis and Applications, 2025, 89
Mariia V. Stefanchuk, “On exponential asymptotics of ring Q-homeomorphisms at infinity”, J Math Sci, 282:1 (2024), 83
Mariia Volodymyrivna Stefanchuk, “On exponential asymptotics of one class of homeomorphisms at a point of the complex plane”, PIGC, 17:2 (2024), 158
Mariia V. Stefanchuk, “On exponential asymptotics of ring Q-homeomorphisms at infinity”, UMB, 21:1 (2024), 107
Izv. Math., 87:4 (2023), 683–725
Igor Petkov, Ruslan Salimov, Mariia Stefanchuk, “On the distortion of the disk image diameter”, UMB, 20:2 (2023), 219
R. Salimov, L. Vyhivska, B. Klishchuk, “Pro spotvorennya transfіnіtnogo dіametra obrazu kruga”, Ukr. Mat. Zhurn., 75:2 (2023), 207
R. Salimov, L. Vyhivska, B. Klishchuk, “On Distortions of the Transfinite Diameter of Disk Image”, Ukr Math J, 75:2 (2023), 235
R. R. Salimov, V. A. Klishchuk, “On the Behavior of One Class of Homeomorphisms at Infinity”, Ukr Math J, 74:10 (2023), 1617
Igor V. Petkov, Ruslan R. Salimov, Mariia V. Stefanchuk, “On the distortion of the disk image diameter”, J Math Sci, 274:3 (2023), 352
Bogdan Klishchuk, Ruslan Salimov, Mariia Stefanchuk, “On the asymptotic behavior at infinity of one mapping class”, PIGC, 16:1 (2023), 50
S. K. Vodopyanov, “Coincidence of set functions in quasiconformal analysis”, Sb. Math., 213:9 (2022), 1157–1186
R. R. Salimov, B. A. Klishchuk, “Pro povedіnku odnogo klasu gomeomorfіzmіv na neskіnchennostі”, Ukr. Mat. Zhurn., 74:10 (2022), 1416
Bogdan A. Klishchuk, “On Power-Law Behavior of Some Mapping Class at Infinity”, J Math Sci, 268:2 (2022), 192
Ruslan Salimov, Bogdan Klishchuk, Trends in Mathematics, Current Trends in Analysis, its Applications and Computation, 2022, 173
S. K. Vodopyanov, A. O. Tomilov, “Functional and analytic properties of a class of mappings in quasi-conformal analysis”, Izv. Math., 85:5 (2021), 883–931
S. K. Vodopyanov, “On the equivalence of two approaches to problems of quasiconformal analysis”, Siberian Math. J., 62:6 (2021), 1010–1025
V. A. Klyachin, N. A. Chebanenko, “O geometricheskikh svoistvakh nepreryvnykh otobrazhenii, sokhranyayuschikh orientatsiyu simpleksov”, Sib. elektron. matem. izv., 18:2 (2021), 985–996
S. K. Vodopyanov, “On the Analytic and Geometric Properties of Mappings in the Theory of Qq,p-Homeomorphisms”, Math. Notes, 108:6 (2020), 889–894
S. K. Vodopyanov, “The regularity of inverses to Sobolev mappings and the theory of Qq,p-homeomorphisms”, Siberian Math. J., 61:6 (2020), 1002–1038
Citation in format AMSBIB
Contact us: