Geodesic
On the boundary behavior of some classes of mappings
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 169-190 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The boundary behavior of closed open discrete mappings of Sobolev and Orlicz–Sobolev classes in $\mathbb R^n$, $n\ge3$, is studied. It is proved that a mapping $f$ mentioned above has a continuous extension to a boundary point $x_0\in\partial D$ of a domain $D\subset\mathbb R^n$ whenever its inner dilatation of order $\alpha>n-1$ has a majorant of finite mean oscillation class at the point in question. Another sufficient condition for continuous extension of mappings is the divergence of some integral. Some results on continuous extension of these mappings to an isolated boundary point are also proved. 
@article{ZNSL_2018_467_a14,
     author = {E. A. Sevost'yanov},
     title = {On the boundary behavior of some classes of mappings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {169--190},
     year = {2018},
     volume = {467},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a14/}
}
TY  - JOUR
AU  - E. A. Sevost'yanov
TI  - On the boundary behavior of some classes of mappings
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2018
SP  - 169
EP  - 190
VL  - 467
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a14/
LA  - ru
ID  - ZNSL_2018_467_a14
ER  - 
%0 Journal Article
%A E. A. Sevost'yanov
%T On the boundary behavior of some classes of mappings
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 169-190
%V 467
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a14/
%G ru
%F ZNSL_2018_467_a14
E. A. Sevost'yanov. On the boundary behavior of some classes of mappings. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 169-190. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a14/

[1] C. J. Bishop, V. Ya. Gutlyanskii, O. Martio, M. Vuorinen, “On conformal dilatation in space”, Intern. Journ. Math. Math. Sci., 22 (2003), 1397–1420 | DOI | MR | Zbl

[2] F. W. Gehring, “Rings and quasiconformal mappings in space”, Trans. Amer. Math. Soc., 103 (1962), 353–393 | DOI | MR | Zbl

[3] V. Gutlyanskii, V. Ryazanov, E. Yakubov, “The Beltrami equations and prime ends”, Ukr. mat. vestnik, 12:1 (2015), 27–66 | MR | Zbl

[4] A. Golberg, R. Salimov, “Topological mappings of integrally bounded $p$-moduli”, Ann. Univ. Buchar. Math. Ser., 3(LXI):1 (2012), 49–66 | MR | Zbl

[5] A. Golberg, R. Salimov, E. Sevost'yanov, “Singularities of discrete open mappings with controlled $p$-module”, J. Anal. Math., 127 (2015), 303–328 | DOI | MR | Zbl

[6] T. Iwaniec, G. Martin, Geometrical Function Theory and Non-Linear Analysis, Clarendon Press, Oxford, 2001 | MR

[7] D. A. Kovtonyuk, V. I. Ryazanov, R. R. Salimov, E. A. Sevostyanov, “K teorii klassov Orlicha–Soboleva”, Algebra analiz, 25:6 (2013), 50–102 | MR | Zbl

[8] D. Kovtonuyk, V. Ryazanov, “New modulus estimates in Orlicz-Sobolev classes”, Ann. Univ. Buchar. Math. Ser., 5(LXIII):1 (2014), 131–135 | MR

[9] O. Martio, V. Ryazanov, U. Srebro, E. Yakubov, Moduli in Modern Mapping Theory, Springer Science, Business Media, LLC, New York, 2009 | MR | Zbl

[10] Yu. G. Reshetnyak, Prostranstvennye otobrazheniya s ogranichennym iskazheniem, Nauka, Novosibirsk, 1982

[11] S. Rickman, Quasiregular mappings, Results in Mathematic and Related Areas (3), 26, Springer-Verlag, Berlin, 1993 | MR | Zbl

[12] M. Vuorinen, “Exceptional sets and boundary behavior of quasiregular mappings in $n$-space”, Ann. Acad. Sci. Fenn. Ser. A1 Math. Dissertationes, 11 (1976), 1–44 | MR

[13] E. A. Sevostyanov, “Ob ustranenii izolirovannykh osobennostei klassov Orlicha–Soboleva s vetvleniem”, Ukr. mat. zhurnal, 68:9 (2016), 1259–1272

[14] E. A. Sevostyanov, R. R. Salimov, E. A. Petrov, “Ob ustranenii osobennostei klassov Orlicha–Soboleva”, Ukr. mat. vestnik, 13:3 (2016), 324–349

[15] K. Kuratovskii, Topologiya, v. 2, Mir, M., 1969

[16] A. P. Calderon, “On the differentiability of absolutely continuous functions”, Riv. Math. Univ. Parma, 2 (1951), 203–213 | MR | Zbl

[17] W. P. Ziemer, “Extremal length and $p$-capacity”, Michigan Math. J., 16 (1969), 43–51 | DOI | MR | Zbl

[18] R. R. Salimov, “Ob otsenke mery obraza shara”, Sib. matem. zhurn., 53:4 (2012), 920–930 | MR | Zbl

[19] D. A. Kovtonyuk, R. R. Salimov, E. A. Sevostyanov, K teorii otobrazhenii klassov Soboleva i Orlicha–Soboleva, ed. V. I. Ryazanov, Naukova dumka, Kiev, 2013