For citation:
Rasulov K. M., Mikhalyova T. I. On a solution of a nondegenerate boundary value problem of Carleman type for quasiharmonic functions in circular domains. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 3, pp. 307-314. DOI: 10.18500/1816-9791-2022-22-3-307-314, EDN: MXESPP
On a solution of a nondegenerate boundary value problem of Carleman type for quasiharmonic functions in circular domains
This paper considers a Carleman type boundary value problem for quasiharmonic functions. The boundary value problem is an informal model of a Carleman type differential problem for analytic functions of a complex variable.This paper presented a complex-analytical method for solving the problem under consideration in circular domains, which makes it possible to establish the instability of its solutions concerning small contour changes.
- Rasulov K. M. Metod sopriazheniya analiticheskikh funktsiy i nekotorye ego prilozheniya [Conjugation Method of Analytic Functions and Some of Its Applications]. Smolensk, SmolSU Publ., 2013. 188 p. (in Russian).
- Rasulov K. M. On the uniqueness of the solution of the Dirichlet boundary value problem for queasiharmonic functions in a non-unit disk. Lobachevskii Journal of Mathematics, 2018, vol. 39, iss. 1, pp. 142—145. https://doi.org/10.1134/S1995080218010237
- Bauer K. W. Uber eine der Differentialgleichung (1+z
z)2Wzz±n(n+1)W = 0 zugeordnete Funktionentheorie. Bonner Mathematische Schriften, 1964, Nr. 23, S. 1–98. - Bauer K. W., Ruscheweyh S. Differential Operators for Partial Differential Equations and Function Theoretic Applications. Berlin, Heidelberg, New York, Springer-Verlag, 1980. 253 p. https://doi.org/10.1007/BFb0103468
- Vekua N. P. Sistemy singuliarnykh integral’nykh uravneniy [Systems of Singular Integral Equations]. Moscow, Nauka, 1970. 379 p. (in Russian).
- Gahov F. D. Kraevye zadachi [Boundary Value Problems]. Moscow, Nauka, 1977. 640 p. (in Russian).
- Litvinchuk G. S. Kraevye zadachi i singuliarnye integral’nye uravneniya so sdvigom [Boundary Value Problems and Singular Integral Equations with Shift]. Moscow, Nauka, 1977. 448 p (in Russian).
- Begehr H. Complex Analytic Methods for Partial Differential Equations. Singapore, World Scientific Publishing, 1994. 273 p.
- Coddington E. A., Levinson N. Theory of Ordinary Differential Equations. McGraw-Hill Companies, 1955. 429 p. (Russ. ed.: Moscow, Foreign Languages Publishing House, 1958. 474 p.).
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