Geodesic
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, Tome 22 (2022) no. 3, pp. 307-314 
K. M. Rasulov; T. I. Mikhalyova. 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, Tome 22 (2022) no. 3, pp. 307-314. http://geodesic.mathdoc.fr/item/ISU_2022_22_3_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Rasulov K. M., Conjugation Method of Analytic Functions and Some of Its Applications, SmolSU Publ, Smolensk, 2013, 188 pp. (in Russian)

[2] 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, 39:1 (2018), 142–145 (PKGXIK) | DOI | MR | Zbl

[3] Bauer K. W., “Über eine der Differentialgleichung $(1+z\overline{z})^2W_{z\overline{z}}\pm n(n+1)W=0$ zugeordnete Funktionentheorie”, Bonner Mathematische Schriften, 1964, no. 23, 1–98 | MR

[4] Bauer K. W., Ruscheweyh S., Differential Operators for Partial Differential Equations and Function Theoretic Applications, Springer-Verlag, Berlin–Heidelberg–New York, 1980, 253 pp. | DOI | MR | Zbl

[5] Vekua N. P., Systems of Singular Integral Equations, Nauka, M., 1970, 379 pp. (in Russian) | MR

[6] Gahov F. D., Boundary Value Problems, Nauka, M., 1977, 640 pp. (in Russian)

[7] Litvinchuk G. S., Boundary Value Problems and Singular Integral Equations with Shift, Nauka, M., 1977, 448 pp. (in Russian)

[8] Begehr H., Complex Analytic Methods for Partial Differential Equations, World Scientific Publishing, Singapore, 1994, 273 pp. | MR | Zbl

[9] Coddington E. A., Levinson N., Theory of Ordinary Differential Equations, McGraw-Hill Companies, 1955, 429 pp. | MR | Zbl