Riemann problem on the double of a multiply connected circular region

V. V. Mityushev

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 1, page 1-14
  • ISSN: 0066-2216

Abstract

top
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.

How to cite

top

V. V. Mityushev. "Riemann problem on the double of a multiply connected circular region." Annales Polonici Mathematici 67.1 (1997): 1-14. <http://eudml.org/doc/270483>.

@article{V1997,
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.},
author = {V. V. Mityushev},
journal = {Annales Polonici Mathematici},
keywords = {boundary value problems on Riemann surfaces; functional equation; Riemann boundary value problem},
language = {eng},
number = {1},
pages = {1-14},
title = {Riemann problem on the double of a multiply connected circular region},
url = {http://eudml.org/doc/270483},
volume = {67},
year = {1997},
}

TY - JOUR
AU - V. V. Mityushev
TI - Riemann problem on the double of a multiply connected circular region
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 1
SP - 1
EP - 14
AB - 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.
LA - eng
KW - boundary value problems on Riemann surfaces; functional equation; Riemann boundary value problem
UR - http://eudml.org/doc/270483
ER -

References

top
  1. [1] B. Bojarski, On a boundary value problem of the theory of functions, Dokl. Akad. Nauk SSSR 119 (1958), 199-202 (in Russian). 
  2. [2] B. Bojarski, On the generalized Hilbert boundary value problem, Soobshch. Akad. Nauk Gruzin. SSR 25 (1960), 385-390 (in Russian). 
  3. [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. [4] F. D. Gakhov, Boundary Value Problems, Nauka, Moscow, 1977 (in Russian). 
  5. [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. [6] M. A. Krasnosel'skiĭ, Approximate Methods for Solution of Operator Equations, Nauka, Moscow, 1969 (in Russian). 
  7. [7] V. V. Mityushev, Solution of the Hilbert boundary value problem for a multiply connected domain, Słupskie Prace Mat.-Przyr. 9a (1994), 37-69. Zbl0818.30026
  8. [8] V. V. Mityushev, Plane problem for steady heat conduction of material with circular inclusions, Arch. Mech. 45 (1993), 211-215. Zbl0785.73055
  9. [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). Zbl0217.10201

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.