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1998 | 68 | 3 | 227-236
Tytuł artykułu

Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The conformal mapping ω(z) of a domain D onto the unit disc must satisfy the condition |ω(t)| = 1 on ∂D, the boundary of D. The last condition can be considered as a Dirichlet problem for the domain D. In the present paper this problem is reduced to a system of functional equations when ∂D is a circular polygon with zero angles. The mapping is given in terms of a Poincaré series.
Rocznik
Tom
68
Numer
3
Strony
227-236
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-02-24
Twórcy
  • Institute of Mathematics, Pedagogical University, Arciszewskiego 22b, 76-200 Slupsk, Poland
Bibliografia
  • [1] T. Akaza, Singular sets of some Kleinian groups, Nagoya Math. J. 26 (1966), 127-143.
  • [2] T. Akaza and K. Inoue, Limit sets of geometrically finite free Kleinian groups, Tôhoku Math. J. 36 (1984), 1-16.
  • [3] S. Axler, P. Bourdon and W. Ramey, Harmonic Function Theory, Springer, New York, 1992.
  • [4] È. N. Bereslavskiĭ, On integrating in closed form of a class of Fuchsian equations and its applications, Differentsial'nye Uravneniya 25 (1989), 1048-1050 (in Russian).
  • [5] B. Bojarski, On the generalized Hilbert boundary value problem, Soobshch. Akad. Nauk Gruzin. SSR 25 (1960), 385-390 (in Russian).
  • [6] F. D. Gakhov, Boundary Value Problems, Pergamon Press, Oxford, 1966.
  • [7] G. M. Golusin, Geometrische Funktionentheorie, Deutscher Verlag Wiss., Berlin 1957.
  • [8] M. A. Krasnosel'skiĭ, Approximate Methods for Solution of Operator Equations, Nauka, Moscow, 1969 (in Russian).
  • [9] S. G. Michlin, Integral Equations, Pergamon Press, New York, 1964.
  • [10] V. V. Mityushev, Plane problem for the steady heat conduction of material with circular inclusions, Arch. Mech. 45 (1993), 211-215.
  • [11] V. V. Mityushev, Solution of the Hilbert problem for a multiply connected domain, Słupskie Prace Mat. Przyr. 9a (1994), 37-69.
  • [12] P. Ya. Polubarinova-Kochina, On additional parameters on the examples of circular 4-polygons, Prikl. Mat. i Mekh. 55 (1991), 222-227 (in Russian).
  • [13] A. R. Tsitskishvili, On construction of analytic functions which map conformally the half-plane onto circular polygons, Differentsial'nye Uravneniya 21 (1985), 646-656 (in Russian).
  • [14] V. I. Vlasov and S. L. Skorokhod, Analytical solution of the Dirichlet problem for the Poisson equation for a class of polygonal domains, Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1988 (in Russian).
  • [15] V. I. Vlasov and D. B. Volkov, The Dirichlet problem in a disk with a corner cut, Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1986 (in Russian).
  • [16] V. I. Vlasov and D. B. Volkov, Solution of the Dirichlet problem for the Poisson equation in some domains with a complex boundary structure, Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1989 (in Russian).
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-apmv68z3p227bwm
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