Riemann problem on the double of a multiply connected circular region

• Autorzy: V. V. Mityushev
• Języki publikacji: EN

Abstrakty

EN

The Riemann problem has been solved in [9] for an arbitrary closed Riemann surface in terms of the principal functionals. This paper is devoted to solution of the problem only for the double of a multiply connected region and can be treated as complementary to [9,1]. We obtain a complete solution of the Riemann problem in that particular case. The solution is given in analytic form by a Poincaré series.

Słowa kluczowe

EN

boundary value problems on Riemann surfaces; functional equation

Kategorie tematyczne

• 30E25: Boundary value problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 67
• Numer: 1
• Strony: 1-14

Daty

wydano

1997

otrzymano

1993-04-05

poprawiono

1996-12-10

Twórcy

autor

V. V. Mityushev

• Department of Mathematics, Pedagogical College, Arciszewskiego 22b, 76-200 Słupsk, Poland

Bibliografia

• [1] B. Bojarski, On a boundary value problem of the theory of functions, Dokl. Akad. Nauk SSSR 119 (1958), 199-202 (in Russian).
• [2] B. Bojarski, On the generalized Hilbert boundary value problem, Soobshch. Akad. Nauk Gruzin. SSR 25 (1960), 385-390 (in Russian).
• [3] B. Bojarski, On the Riemann-Hilbert problem for a multiply connected domain, in: I. N. Vekua, Generalized Analytic Functions, Nauka, Moscow, 1988 (in Russian).
• [4] F. D. Gakhov, Boundary Value Problems, Nauka, Moscow, 1977 (in Russian).
• [5] G. M. Goluzin, Solution of the plane problem of steady heat conduction for multiply connected domains which are bounded by circumferences, Mat. Sb. 42 (1935), 191-198 (in Russian).
• [6] M. A. Krasnosel'skiĭ, Approximate Methods for Solution of Operator Equations, Nauka, Moscow, 1969 (in Russian).
• [7] V. V. Mityushev, Solution of the Hilbert boundary value problem for a multiply connected domain, Słupskie Prace Mat.-Przyr. 9a (1994), 37-69.
• [8] V. V. Mityushev, Plane problem for steady heat conduction of material with circular inclusions, Arch. Mech. 45 (1993), 211-215.
• [9] È. I. Zverovich, Boundary value problems of the theory of analytic functions in Hölder classes on Riemann surfaces, Uspekhi Mat. Nauk 26 (1) (1971), 113-179 (in Russian).