About space mappings with integral restrictions on the characteristics

E. A. Sevostyanov

Algebra i analiz, Tome 24 (2012) no. 1, pp. 131-156.

Bibliographie

[1] Alfors L., Lektsii po kvazikonformnym otobrazheniyam, Mir, M., 1969 | MR

[2] Biluta P. A., “Nekotorye ekstremalnye zadachi dlya otobrazhenii, kvazikonformnykh v srednem”, Sib. mat. zh., 6:4 (1965), 717–726 | MR | Zbl

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

[4] Bourbaki N., Functions of a real variable, Springer, Berlin, 2004 | MR

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

[6] Golberg A., “Homeomorphisms with finite mean dilatations”, Complex Analysis and Dynamical Systems, v. II, Contemp. Math., 382, Amer. Math. Soc., Providence, RI, 2005, 177–186 | DOI | MR | Zbl

[7] Goldshtein V. M., Reshetnyak Yu. G., Vvedenie v teoriyu funktsii s obobschennymi proizvodnymi i kvazikonformnye otobrazheniya, Nauka, M., 1983 | MR

[8] Kruglikov V. I., “Emkosti kondensatorov i prostranstvennye otobrazheniya, kvazikonformnye v srednem”, Mat. sb., 130(172):2 (1986), 185–206 | MR | Zbl

[9] Krushkal S. L., “Ob otobrazheniyakh, kvazikonformnykh v srednem”, Dokl. AN SSSR, 157:3 (1964), 517–519 | Zbl

[10] Lehto O., Virtanen K., Quasiconformal mappings in the plane, Grundlehren Math. Wiss., 126, Springer, New York etc., 1973 | MR | Zbl

[11] Martio O., Ryazanov V., Srebro U., Yakubov E., Moduli in modern mapping theory, Springer, New York, 2009 | MR | Zbl

[12] Miklyukov V. M., Konformnoe otobrazhenie neregulyarnoi poverkhnosti i ego primeneniya, VolGU, Volgograd, 2005

[13] Perović M., “Isolated singularity of the mean quasiconformal mappings”, Romanian-Finnish Seminar on Complex Analysis (Bucharest, 1976), Lecture Notes in Math., 743, Springer, Berlin, 1979, 212–214 | DOI | MR

[14] Pesin I. N., “Otobrazheniya, kvazikonformnye v srednem”, Dokl. AN SSSR, 187:4 (1969), 740–742 | MR | Zbl

[15] Poletskii E. A., “Metod modulei dlya negomeomorfnykh kvazikonformnykh otobrazhenii”, Mat. sb., 83(125):2 (1970), 261–272 | MR | Zbl

[16] Reshetnyak Yu. G., Prostranstvennye otobrazheniya s ogranichennym iskazheniem, Nauka, Novosibirsk, 1982 | MR | Zbl

[17] Rickman S., Quasiregular mappings, Ergeb. Math. Grenzgeb. (3), 26, Springer-Verlag, Berlin, 1993 | MR | Zbl

[18] Ryazanov V. I., “Ob otobrazheniyakh, kvazikonformnykh v srednem”, Sib. mat. zh., 37:2 (1996), 378–388 | MR | Zbl

[19] Ryazanov V., Srebro U., Yakubov E., “On integral conditions in the mapping theory”, Ukr. Mat. Visn., 7:1 (2010), 73–87 | MR

[20] Strugov Yu. F., “O kompaktnosti semeistv otobrazhenii, kvazikonformnykh v srednem”, Dokl. AN SSSR, 243:4 (1978), 859–861 | MR | Zbl

[21] Suvorov G. D., Ob iskusstve matematicheskogo issledovaniya, Donetskaya firma naukoemkikh tekhnologii NAN Ukrainy (Firma TEAN), Donetsk, 1999

[22] Väisälä J., Lectures on $n$-dimensional quasiconformal mappings, Lecture Notes in Math., 229, Springer-Verlag, Berlin etc., 1971 | MR

[23] Ukhlov A., Vodopyanov S. K., “Mappings associated with weighted Sobolev spaces”, Complex Analysis and Dynamical Systems, v. III, Contemp. Math., 455, Amer. Math. Soc., Providence, RI, 2008, 369–382 | DOI | MR | Zbl

[24] Zorich V. A., “O dopustimom poryadke rosta kharakteristiki kvazikonformnosti v teoreme M. A. Lavrenteva”, Dokl. AN SSSR, 181:3 (1968), 530–533 | Zbl

[25] Sevostyanov E. A., “Ob integralnoi kharakterizatsii nekotorykh obobschenii kvaziregulyarnykh otobrazhenii i znachenii usloviya raskhodimosti integrala v geometricheskoi teorii funktsii”, Ukr. mat. zh., 61:10 (2009), 1367–1380

[26] Sevostyanov E. A., “O tochkakh vetvleniya otobrazhenii s neogranichennoi kharakteristikoi kvazikonformnosti”, Sib. mat. zh., 51:5 (2010), 1129–1146 | MR

[27] Sevostyanov E. A., “Obobschenie odnoi lemmy E. A. Poletskogo na klassy prostranstvennykh otobrazhenii”, Ukr. mat. zh., 61:7 (2009), 969–975 | MR