Year: 2024
Type: article
Abstract: In this paper, we investigate some boundary value problems for the Cauchy–Riemann equations in the triangular domain M. By the parqueting-reflection method, we obtain a covering of the complex plane through reflections of the domain. Then by the Cauchy–Pompeiu formula, we derive the Cauchy–Schwarz representation formula in M. In addition, we consider the Schwarz boundary value problem for the inhomogeneous Cauchy–Riemann equation and the explicit expressions of solution and condition of solvability. Finally, by using the Schwarz boundary value problem, the solution of the Dirichlet boundary value problem is explicitly solved.
Source: Russian Mathematics
Authors: A. Darya, N. Taghizadeh
Institution: University of Guilan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4405016978