Inequalities for Inner Radii of Disjoint Domains and Open Sets
Informatics and Automation, Differential equations and dynamical systems, Tome 261 (2008), pp. 37-46.

Voir la notice de l'article provenant de la source Math-Net.Ru

In geometric function theory there is a well-known field related to estimates for functionals that depend on the inner radii of nonoverlapping domains. Many authors has contributed to the development of this field. Today, great attention is being paid to the study of extremal problems for nonoverlapping domains with free poles. In this paper, one result of this kind is generalized and strengthened.
@article{TRSPY_2008_261_a3,
     author = {A. K. Bakhtin},
     title = {Inequalities for {Inner} {Radii} of {Disjoint} {Domains} and {Open} {Sets}},
     journal = {Informatics and Automation},
     pages = {37--46},
     publisher = {mathdoc},
     volume = {261},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a3/}
}
TY  - JOUR
AU  - A. K. Bakhtin
TI  - Inequalities for Inner Radii of Disjoint Domains and Open Sets
JO  - Informatics and Automation
PY  - 2008
SP  - 37
EP  - 46
VL  - 261
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a3/
LA  - ru
ID  - TRSPY_2008_261_a3
ER  - 
%0 Journal Article
%A A. K. Bakhtin
%T Inequalities for Inner Radii of Disjoint Domains and Open Sets
%J Informatics and Automation
%D 2008
%P 37-46
%V 261
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a3/
%G ru
%F TRSPY_2008_261_a3
A. K. Bakhtin. Inequalities for Inner Radii of Disjoint Domains and Open Sets. Informatics and Automation, Differential equations and dynamical systems, Tome 261 (2008), pp. 37-46. http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a3/

[1] Lavrentev M. A., “K teorii konformnykh otobrazhenii”, Tr. Fiz.-mat. in-ta AN SSSR, 5 (1934), 159–245

[2] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR | Zbl

[3] Dzhenkins Dzh. A., Odnolistnye funktsii i konformnye otobrazheniya, Izd-vo inostr. lit., M., 1962

[4] Lebedev N. A., Printsip ploschadei v teorii odnolistnykh funktsii, Nauka, M., 1975 | MR | Zbl

[5] Bakhtina G. P., Variatsionnye metody i kvadratichnye differentsialy v zadachakh o nenalegayuschikh oblastyakh, Avtoref. dis. $\dots$ kand. fiz.-mat. nauk, Kiev, 1975, 11 pp.

[6] Dubinin V. N., Emkosti kondensatorov v geometricheskoi teorii funktsii, Izd-vo Dalnevost. un-ta, Vladivostok, 2003

[7] Dubinin V. N., “Asimptotika modulya vyrozhdayuschegosya kondensatora i nekotorye primeneniya”, Zap. nauch. sem. POMI, 237, 1997, 56–73 | MR | Zbl

[8] Dubinin V. N., “Simmetrizatsiya v geometricheskoi teorii funktsii kompleksnogo peremennogo”, UMN, 49:1 (1994), 3–76 | MR | Zbl

[9] Kuzmina G. V., “Metody geometricheskoi teorii funktsii. I”, Algebra i analiz, 9:3 (1997), 41–103 | MR

[10] Kuzmina G. V., “Metody geometricheskoi teorii funktsii. II”, Algebra i analiz, 9:5 (1997), 1–50 | MR

[11] Emelyanov E. G., “O svyazi dvukh zadach ob ekstremalnom razbienii”, Zap. nauch. sem. LOMI, 160, 1987, 91–98 | MR

[12] Bakhtin A. K., “Kusochno razdelyayuschee preobrazovanie i ekstremalnye zadachi so svobodnymi polyusami na luchakh”, Dop. NAN Ukraïni, 2004, no. 12, 7–13 | MR | Zbl

[13] Kovalev L. V., “O vnutrennikh radiusakh simmetrichnykh nenalegayuschikh oblastei”, Izv. vuzov. Matematika, 2000, no. 6, 80–81 | MR | Zbl

[14] Gromova L. L., Lebedev N. A., “O nenalegayuschikh oblastyakh, lezhaschikh v kruge. II”, Vestn. Leningr. un-ta, 1973, no. 1, 25–36 | MR | Zbl

[15] Bakhtin A. K., “Kusochno razdelyayuschee preobrazovanie i ekstremalnye zadachi so svobodnymi polyusami”, DAN, 405:2 (2005), 151–153 | MR | Zbl

[16] Kolbina L. I., “Konformnoe otobrazhenie edinichnogo kruga na nenalegayuschie oblasti”, Vestn. Leningr. un-ta, 1955, no. 5, 37–43 | MR | Zbl

[17] Dubinin V. N., “Razdelyayuschee preobrazovanie oblastei i zadachi ob ekstremalnom razbienii”, Zap. nauch. sem. LOMI, 168, 1988, 48–66 | Zbl

[18] Kuzmina G. V., “Metod ekstremalnoi metriki v zadachakh o maksimume proizvedeniya stepenei konformnykh radiusov nenalegayuschikh oblastei pri nalichii svobodnykh parametrov”, Zap. nauch. sem. POMI, 302, 2003, 52–67 | MR

[19] Kheiman V. K., Mnogolistnye funktsii, Izd-vo inostr. lit., M., 1960 | MR

[20] Tamrazov P. M., Subgarmonicheskie funktsii v konturno-telesnoi zadache, Preprint IM-85-47, Kiev, 1985, 24 pp. | MR