This article is cited in 2 papers

On Cauchy problem solution for a harmonic function in a simply connected domain

E. A. Shirokova, P. N. Ivanshin

Lobachevskiy Institute of Mathematics & Mechanics, Kazan Federal University, Kremlevskaya st., 35, Kazan, 420008, Russia

Abstract: Here we present an investigation of the Cauchy problem solvability for the Laplace equation in a simply connected plane domain. The investigation is reduced to solution of two singular integral equations. If the problem is resolvable, its solution can be restored via the integral Cauchy formula. Examples of the solvable and unsolvable problems are presented. The construction involves the auxiliary approximate conformal mapping.

Keywords: Cauchy problem, integral equation, holomorphic function, spline, approximate solution.

UDC: 517.956.223

MSC: 30-08

Received: 20.08.2022
Revised: 24.02.2023
Accepted: 23.02.2023

Language: English

DOI: 10.15393/j3.art.2023.12230