On a new condition of finite Lipschitz of Orlicz-Sobolev class(in Russian) |
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| Author |
ruslan623@yandex.ru, salimov07@rambler.ru
Institute of Mathematics
Ukrainian National Academy of Sciences, Kyiv
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| Abstract |
It is found a new sufficient condition of finite Lipschitz in terms of inner dilation for homeomorphisms of
the Orlicz-Sobolev class $W_{{\rm loc}}^{1,\varphi}$ under a condition of the Calderon type on $\varphi$.
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| Keywords |
$p$-moduli of the families of curves, $p$-moduli of the families of surfaces, mappings of finite distortion,
Sobolev classes, Orlicz–Sobolev classes, local Lipschitz, finite Lipschitz
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| DOI |
doi:10.15330/ms.44.1.27-35
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| Reference |
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P. 175–193.
2. Iwaniec T., Sverak V. On mappings with integrable dilatation// Proc. Amer. Math. Soc. – 1993. – V.118. – P. 181–188. 3. Iwaniec T., Martin G. Geometrical function theory and non-linear analysis. – Clarendon Press, Oxford, 2001. 4. Salimov R.R. On finite Lipschitz Orlicz–Sobolev classes// Vladikavkaz. Mat. Zh. – 2015. – V.17, ¹1. – P. 64–77. (in Russian) 5. Reshetnyak, Yu.G. Spatial mappings with bounded distortion. – Nauka, Novosibirsk, 1982. (in Russian) 6. Krasnosel’skii M.A., Rutickii Ja.B. Convex functions and Orlicz spaces. – Problems of Contemporary Mathematics Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1958. (in Russian) 7. Mazia V.H. Sobolev spaces. – Leningrad Univ., Leningrad. – 1985. (in Russian) 8. Iwaniec T., Koskela P., Onninen J. Mappings of finite distortion: Compactness// Ann. Acad. Sci. Fenn. Ser. A1. Math. – 2002. – V.27, ¹2. – P. 391–417. 9. Kovtonyuk D.A., Ryazanov V.I., Salimov R.R., Sevost’yanov E.A. To the theory of the mappings of Sobolev and Orlicz–Sobolev classes. – Naukova Dumka, Kyiv, 2013. (in Russian) 10. Kovtonyuk D.A., Ryazanov V.I., Salimov R.R., Sevost’yanov E.A. Toward the theory of the Orlicz- Sobolev classes// Algebra i Analiz. – 2013. - V.25, ¹6. - P. 50–102. (in Russian) 11. Vaisala J. Two new characterizations for quasiconformality// Ann. Acad. Sci. Fenn. Ser. A1 Math. – 1965. – V.362. – P. 1–12. 12. Martio O., Ryazanov V., Srebro U., Yakubov E. Moduli in modern mapping theory// Springer Monographs in Mathematics. – Springer, New York etc, 2009. 13. Menchoff D. Sur les differencelles totales des fonctions univalentes// Math. Ann. – 1931. – V.105. – P. 75–85. 14. Gehring F.W., Lehto O. On the total differentiability of functions of a complex variable// Ann. Acad. Sci. Fenn. Ser. A1. Math. – 1959. – V.272. – P. 3–8. 15. Lehto O., Virtanen K. Quasiconformal mappings in the plane. – Springer–Verlag, New York, 1973. 16. Golberg A., Salimov R. Topological mappings of integrally bounded p–moduli// Ann. Univ. Bucharest, Ser. Math. - 2012. - V.3(LXI), ¹1. - P. 49–66. 17. Salimov R. One property of ring Q-homeomorphisms with respect to a p-module// Ukr. Math. Journal - 2013. - V.65, ¹5.- P. 728–733. (in Russian) 18. Saks S. Theory of the integral. – IL, M., 1949. (in Russian) 19. Federer G. Geometric measure theory. – Nauka, Moscow, 1987. (in Russian) 20. Sevost’yanov E.A. Investigation of space mappings by geometric method. – Naukova Dumka, Kyiv, 2014. (in Russian) |
| Pages |
27-35
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| Volume |
44
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| Issue |
1
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| Year |
2015
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |