# Riemann problem on the double of a multiply connected circular region

Annales Polonici Mathematici (1997)

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

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topV. 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] 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. Zbl0818.30026
- [8] V. V. Mityushev, Plane problem for steady heat conduction of material with circular inclusions, Arch. Mech. 45 (1993), 211-215. Zbl0785.73055
- [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

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