On continuous extensions of Orlicz-Sobolev classes

O. S. Afanasieva; R. R. Salimov

doi:10.15330/ms.45.1.34-39

1. Afanasieva E.S., Ryazanov V.I., Salimov R.R. On mappings in the Orlicz-Sobolev classes on Riemannian manifolds// Ukr. Mat. Visn. - 2011. - V.8, №3. - P. 319-342. (in Russian)

2. Kovtonyuk D.A., Salimov R.R., Sevostyanov E.A. To the theory of the mappings of Sobolev and Orlicz-Sobolev classes. - Naukova Dumka, Kyiv, 2013. (in Russian)

3. Kovtonyuk D.A., Ryazanov V.I., Salimov R.R., Sevostyanov E.A. Toward the theory of the Orlicz-Sobolev classes// Algebra i Analiz. - 2013. - V.25, №6. - P. 50-102. (in Russian)

4. Sevostyanov E.A. On the boundary behavior of open discrete mappings with unbounded characteristic// Ukr. Math. J. - 2012. - V.64, №6. - P. 855-859. (in Russian)

5. Il'yutko D.P., Sevostyanov E.A. On local properties of one class of mappings on Riemannian manifolds// Ukr. Mat. Visn. - 2015. - V.12, №2. - P. 210-221. (in Russian)

6. Iwaniec T., Sverak V. On mappings with integrable dilatation// Proc. Amer. Math. Soc. - 1993. - V.118. - P. 181-188.

7. Iwaniec T., Martin G., Geometrical function theory and non-linear analysis, Oxford: Clarendon Press, 2001.

8. Krasnoselskij M.A., Rutitskij Ja.B., Convex functions and Orlicz spaces. - Moscow: Nauka, 1958. (in Russian)

9. Maz’ya V., Sobolev classes. – Berlin: Springer-Verlag, 1985.

10. Martio O., Ryazanov V., Srebro U., Yakubov E., Moduli in modern mapping theory. – New York: Springer, 2009. – 367 p.

11. Golberg A., Salimov R. Topological mappings of integrally bounded p–moduli// Ann. Univ. Bucharest, Ser. Math. – 2012. – V.3(LXI), №1. – P. 49–66.

12. Kovtonyuk D., Ryazanov V. On the theory of lower Q-homeomorphisms// Ukr. Mat. Visn. – 2008. – V.5, №2. – P. 159–184. (in Russian); translated in Ukrainian Math. Bull. by AMS.

13. Shlyk V.A. On the equality between p.capacity and p.modulus// Sibirsk. Mat. Zh. – 1993. – V.34, №6. – P. 216–221; transl. in Siberian Math. J. – 1993. – V.34, №6. – P. 1196–1200.

14. Ziemer W.P. Extremal length and p-capacity// Michigan Math. J. – 1969. – V.16. – P. 43–51.

15. Salimov R.R. On a new condition of finite Lipschitz of Orlicz-Sobolev class// Mat. Stud. – 2015. – V.44, №1. – P. 27—35. (in Russian)

	On continuous extensions of Orlicz-Sobolev classes (in Russian)
Author	O. S. Afanasieva, R. R. Salimov smolka21@yandex.ru; ruslan623@yandex.ru Institute of Applied Mathematics and Mechanics, Slavyansk; Institute of Mathematics, National Academy of Sciences of Ukraine
Abstract	The problem of continuous extension to the boundary of mappings from Orlicz-Sobolev classes between domains is investigated in Euclidean space.
Keywords	boundary behavior; Orlicz-Sobolev classes; p-modulus; Q-homeomorphism
DOI	doi:10.15330/ms.45.1.34-39
Reference	1. Afanasieva E.S., Ryazanov V.I., Salimov R.R. On mappings in the Orlicz-Sobolev classes on Riemannian manifolds// Ukr. Mat. Visn. - 2011. - V.8, №3. - P. 319-342. (in Russian) 2. Kovtonyuk D.A., Salimov R.R., Sevostyanov E.A. To the theory of the mappings of Sobolev and Orlicz-Sobolev classes. - Naukova Dumka, Kyiv, 2013. (in Russian) 3. Kovtonyuk D.A., Ryazanov V.I., Salimov R.R., Sevostyanov E.A. Toward the theory of the Orlicz-Sobolev classes// Algebra i Analiz. - 2013. - V.25, №6. - P. 50-102. (in Russian) 4. Sevostyanov E.A. On the boundary behavior of open discrete mappings with unbounded characteristic// Ukr. Math. J. - 2012. - V.64, №6. - P. 855-859. (in Russian) 5. Il'yutko D.P., Sevostyanov E.A. On local properties of one class of mappings on Riemannian manifolds// Ukr. Mat. Visn. - 2015. - V.12, №2. - P. 210-221. (in Russian) 6. Iwaniec T., Sverak V. On mappings with integrable dilatation// Proc. Amer. Math. Soc. - 1993. - V.118. - P. 181-188. 7. Iwaniec T., Martin G., Geometrical function theory and non-linear analysis, Oxford: Clarendon Press, 2001. 8. Krasnoselskij M.A., Rutitskij Ja.B., Convex functions and Orlicz spaces. - Moscow: Nauka, 1958. (in Russian) 9. Maz’ya V., Sobolev classes. – Berlin: Springer-Verlag, 1985. 10. Martio O., Ryazanov V., Srebro U., Yakubov E., Moduli in modern mapping theory. – New York: Springer, 2009. – 367 p. 11. Golberg A., Salimov R. Topological mappings of integrally bounded p–moduli// Ann. Univ. Bucharest, Ser. Math. – 2012. – V.3(LXI), №1. – P. 49–66. 12. Kovtonyuk D., Ryazanov V. On the theory of lower Q-homeomorphisms// Ukr. Mat. Visn. – 2008. – V.5, №2. – P. 159–184. (in Russian); translated in Ukrainian Math. Bull. by AMS. 13. Shlyk V.A. On the equality between p.capacity and p.modulus// Sibirsk. Mat. Zh. – 1993. – V.34, №6. – P. 216–221; transl. in Siberian Math. J. – 1993. – V.34, №6. – P. 1196–1200. 14. Ziemer W.P. Extremal length and p-capacity// Michigan Math. J. – 1969. – V.16. – P. 43–51. 15. Salimov R.R. On a new condition of finite Lipschitz of Orlicz-Sobolev class// Mat. Stud. – 2015. – V.44, №1. – P. 27—35. (in Russian)
Pages	34-39
Volume	45
Issue	1
Year	2016
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

On continuous extensions of Orlicz-Sobolev classes (in Russian)