On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk-Reference-Cited by-同舟云学术

On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk

Published:2023-10-20 Issue:20 Volume:11 Page:4360
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Bagapsh Astamur¹²,Soldatov Alexandre¹²³

Affiliation:

1. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 40 Vavilova St., Moscow 119333, Russia

2. Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russia

3. Department of Hiah Mathematics, Moscow Power Engineering Institute, National Research University, 14 Krasnokazarmennaya St., Moscow 111250, Russia

Abstract

The role played by explicit formulas for solving boundary value problems for elliptic equations and systems is well known. In this paper, explicit formulas for a general solution of the Dirichlet problem for second-order elliptic systems in the unit disk are given. In addition, an iterative method for solving this problem for systems with respect to two unknown functions is described, and an integral representation of the Poisson type is obtained by applying this method.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/20/4360/pdf

Reference33 articles.

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4. Elliptic systems of high order;Soldatov;Differ. Uravn.,1989

5. Soldatov, A.P. (1997, January 3–7). To elliptic theory for domains with piecewise smooth boundary on the plane. Proceedings of the Congress ISAAC’97, Newark, NJ, USA.