This is a preview of subscription content, log in via an institution to check access.
References
M. V. Keldysh and L. I. Sedov, “Effective solution of some boundary value problems for harmonic functions,” Dokl. Akad. Nauk SSSR,16, No. 1, 7–10 (1937).
N. I. Muskhelishvili, Singular Integral Equations (Boundary Value Problems of the Theory of Functions and Some of Their Applications to Mathematical Physics) [in Russian], Nauka, Moscow (1968).
I. A. Aleksandrov and A. S. Sorokin, “The Schwartz problem for multiply connected circular domains,” Sibirsk. Mat. Zh.,13, No. 5, 971–1001 (1972).
H. Villat, “Le probleme de Dirichlet dans une aire annulaire,” Rend. Circ. Mat. Palermo (2),33, 134–175 (1912).
F. D. Gakhov, Boundary Value Problems [in Russian], Nauka, Moscow (1977).
I. A. Aleksandrov and A. S. Sorokin, “On extension propagation of the Goluzin-Kufarev variational method on multiply connected domains,” Dokl. Akad. Nauk SSSR,16, No. 6, 1207–1210 (1967).
A. S. Sorokin, “Extension of the Kufarev variational theorem on multiply connected domains,” in: Problems of the Geometric Theory of Functions [in Russian],189, No. 4, 1966, pp. 221–231 (Trudy Tomsk. Univ.).
A. S. Sorokin, “The Goluzin-Kufarev variational method and the Keldysh-Sedov formula,” Dokl. Akad. Nauk SSSR,308, No. 2, 273–277 (1989).
H. Meschkowski, “Verallgemeinerung der Poissonschen Integralformel auf mehrfach zusammenhängende Bereiche,” Ann. Acad. Sci. Fenn. Ser. AI Math., No. 166, 64–85 (1954).
V. A. Zmorovich, “On a generalization of the integral Schwartz formula onn-connected circular domains,” Dokl. Akad. Nauk SSSR,16, No. 5, 489–492 (1958).
L. A. Aksent'ev, “A construction of the Schwartz operator by the symmetry method,” Trudy Sem. on Inverse Boundary Value Problems [in Russian], Kazan. Univ., Kazan', 1964, No. 2, pp. 3–11.
A. S. Sorokin, “The homogeneous Keldysh-Sedov problem for multiply connected circular domains in the Muskhelishvili function class,” Differentsial'nye Uravneniya,25, No. 2, 283–293 (1989).
A. S. Sorokin, “The Keldysh-Sedov problem for multiply connected circular domains,” Dokl. Akad. Nauk SSSR,293, No. 1, 41–44;296, No. 4, 801–804 (1987).
G. M. Goluzin, “Solution of basic plane problems of mathematical physics for the case of the Laplace equation and multiply connected domains bounded by circles (the method of functional equations),” Mat. Sb.,41, No. 1, 246–276 (1934).
L. E. Dunduchenko, “More on the Schwartz formula for an-connected circular domain,” Dokl. Akad. Nauk SSSR, No. 11, 1383–1386 (1966).
R. Coifman and G. Weiss, “A kernel associated with certain multiply connected domains and its applications to factorization theorems,” Studia Math.,28, No. 1, 31–68 (1966).
A. E. Khoperskov, “On flows of a fluid with formation of closed cavitational cavities,” Prikl. Mekhanika i Tekhn. Fizika, No. 5, 54–61 (1963).
M. A. Lavrent'ev and B. V. Shabat, Methods of the Theory of Functions of Complex Variables Nauka, Moscow-Leningrad (1973).
Author information
Authors and Affiliations
Additional information
Translated from Sibirskii Matematicheskii, Vol. 36, No. 1, pp. 186–202, January–February, 1995.
Rights and permissions
About this article
Cite this article
Sorokin, A.S. The Keldysh-Sedov problem for multiply connected circular domains. Sib Math J 36, 168–184 (1995). https://doi.org/10.1007/BF02113931
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02113931