Download PDF - Riemann problem on the double of a multiply connected circular regionAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Riemann problem on the double of a multiply connected circular region

Authors 1

Affiliations

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

Abstract

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.

Keywords

ENG
boundary value problems on Riemann surfaces, functional equation

Bibliography

  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).
Annales Polonici Mathematici
1997/67/1
Export to PBN, Opens in new tab
Pages:
1-14
Main language of publication
English
Received
1993-04-05
Accepted
1996-12-10
Published
1997
Exact and natural sciences