Geodesic
On the solution of the Poincare boundary value problem for generalised harmonic functions in simply connected domains
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2024), pp. 6-15.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, a boundary value problem of the Poincare type is considered for one second-order elliptic differential equation, generating a class of generalised harmonic functions, in simply connected domains with smooth boundaries. It is established that for sufficiently general assumptions about the coefficients of the boundary value condition of the considered problem, its solution reduces to the sequential solution of the well-studied integro-differential Hilbert boundary value problem and the differential Hilbert boundary value problem in classes of analytic functions of a complex variable. In addition, necessary and sufficient solvability conditions of the considered problem are obtained and its Noetherian property is proved.
Keywords: Differential equation; generalised harmonic function; Poincare boundary value problem; generalised Hilbert boundary value problem; integral equation; simply connected domain 
@article{BGUMI_2024_1_a0,
     author = {T. R. Nagornaya and K. M. Rasulov},
     title = {On the solution of the {Poincare} boundary value problem for generalised harmonic functions in simply connected domains},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {6--15},
     publisher = {mathdoc},
     volume = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2024_1_a0/}
}
TY  - JOUR
AU  - T. R. Nagornaya
AU  - K. M. Rasulov
TI  - On the solution of the Poincare boundary value problem for generalised harmonic functions in simply connected domains
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2024
SP  - 6
EP  - 15
VL  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2024_1_a0/
LA  - ru
ID  - BGUMI_2024_1_a0
ER  - 
%0 Journal Article
%A T. R. Nagornaya
%A K. M. Rasulov
%T On the solution of the Poincare boundary value problem for generalised harmonic functions in simply connected domains
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2024
%P 6-15
%V 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BGUMI_2024_1_a0/
%G ru
%F BGUMI_2024_1_a0
T. R. Nagornaya; K. M. Rasulov. On the solution of the Poincare boundary value problem for generalised harmonic functions in simply connected domains. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2024), pp. 6-15. http://geodesic.mathdoc.fr/item/BGUMI_2024_1_a0/

[1] T. R. Nagornaya, K. M. Rasulov, “Algoritm yavnogo resheniya zadachi Puankare dlya obobschennykh garmonicheskikh funktsii vtorogo poryadka v krugovykh oblastyakh”, Nauchno-tekhnicheskii vestnik Povolzhya, 11 (2022), 24–27

[2] K. W. Bauer, Uber eine der Differentialgleichung zugeordnete Funktionentheorie, Bonner mathematische Schriften, 23, 1965, 98 pp.

[3] K. W. Bauer, S. Ruscheweyh, Differential operators for partial differential equations and function theoretic applications, Lecture notes in mathematics, 791, Springer-Verlag, Berlin, 1980, 5+258 pp. | DOI

[4] T. R. Nagornaya, K. M. Rasulov, “O kraevoi zadache Puankare dlya obobschennykh garmonicheskikh funktsii v krugovykh oblastyakh”, Nauchno-tekhnicheskii vestnik Povolzhya, 7 (2022), 32–35

[5] K. M. Rasulov, T. R. Nagornaya, “O reshenii v yavnom vide kraevoi zadachi Neimana dlya differentsialnogo uravneniya Bauera v krugovykh oblastyakh”, Izvestiya Saratovskogo universiteta. Novaya seriya. Seriya. Matematika. Mekhanika. Informatika, 21(3) (2021), 326–335 | DOI

[6] A. V. Bitsadze, Uravneniya matematicheskoi fiziki, Nauka, Moskva, 1976, 295 pp.

[7] F. D. Gakhov, “Kraevye zadachi”, 3-e izdanie, Nauka (Moskva), 1977

[8] N. I. Muskhelishvili, Singulyarnye integralnye uravneniya: granichnye zadachi teorii funktsii i nekotorye ikh prilozheniya k matematicheskoi fizike. 3-e izdanie, Nauka, Moskva, 1968, 511 pp.