The Riemann Boundary Value Problem for Generalized Analytical Functions with Supersingular Points on the Contour of the Boundary Condition

被引：0

作者：

Shabalin, P. L. ^{[1
]}

机构：

[1] Kazan State Univ Architecture & Engn, Kazan 420043, Russia

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2024年 / 45卷 / 10期

基金：

俄罗斯科学基金会;

关键词：

generalized analytical functions; supersingular points; Riemann boundary value problem; infinite index; SYSTEM; SHELLS;

D O I：

10.1134/S1995080224605964

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the Riemann boundary value problem with a boundary condition on the real axis for solutions of the generalized Cauchy-Riemann equation in a situation where the coefficient of the equation has n discontinuities of the second kind. We have obtained a formula for the general solution of the generalized Cauchy-Riemann equation. For limited solutions of this equation, we considered the Riemann boundary value problem with a finite index. We have reduced this Riemann boundary value problem to a similar problem for analytical functions with n points of vorticity and an infinite index. Based on these results, we have described the solvability of the Riemann problem for generalized analytical functions.

引用

页码：5244 / 5253

页数：10

共 22 条

[11]

Rasulov A.B., Integral representations and the linear conjugation problem for a generalized Cauchy–Riemann system with a singular manifold, Differ. Equat, 36, pp. 306-312, (2000)

[12]

Shabalin P.L., Faizov R.R., The Riemann problem with a condition on the real axis for generalized analytic functions with a singular curve, Sib. Math. J, 64, pp. 431-442, (2023)

[13]

Shabalin P.L., Faizov R.R., The Riemann problem in a half-plane for generalized analytic functions with a singular line, Russ. Math, 67, pp. 66-75, (2023)

[14]

Gakhov F.D., Boundary Value Problems, (1990)

[15]

Gakhov F.D., Boundary Value Problems, (1990)

[16]

Sandrygailo I.E., ‘On the Riemann boundary value with infinite index for a half-plane, Dokl. Akad. Nauk Belor. SSR, 19, pp. 872-875, (1975)

[17]

Sandrygailo I.E., On the Riemann boundary value with infinite index for a half-plane, Dokl. Akad. Nauk Belor. SSR, 19, pp. 872-875, (1975)

[18]

Tolochko M.E., On the solvability of homogeneous Riemann boundary value problem with infinite index for half-plane,” Dokl. Akad. Nauk Belor. SSR, Ser. Fiz.-, Mat, 10, pp. 872-875, (1975)

[19]

Monakhov V.N., Semenko E.V., Boundary Value Problems and Pseudodifferential Operators on Riemannian Surfaces, (2003)

[20]

Salimov R.B., Karabasheva E.N., The new approach to solving the Riemann boundary value problem with infinite index,” Izv. Sarat. Univ, Nov. Ser. Ser.: Mat. Mekh. Inform, 14, pp. 155-165, (2014)

← 1 2 3 →