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

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