On the solution of the exterior dirichlet problem for an axisymmetric potential

被引：0

作者：

Plaksa S.A. ^{[1
]}

机构：

[1] Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

来源：

Ukrainian Mathematical Journal | 2002年 / 54卷 / 12期

关键词：

Integral Equation; Explicit Form; Unit Circle; Additional Condition; Dirichlet Problem;

D O I：

10.1023/A:1024073231378

中图分类号：

学科分类号：

摘要：

For an unbounded domain of the meridian plane with bounded smooth boundary that satisfies certain additional conditions, we develop a method for the reduction of the Dirichlet problem for an axisymmetric potential to Fredholm integral equations. In the case where the boundary of the domain is a unit circle, we obtain a solution of the exterior Dirichlet problem in explicit form. © 2002 Plenum Publishing Corporation.

引用

页码：1982 / 1991

页数：9

共 50 条

[31] A sign-changing solution for a superlinear Dirichlet problem
Castro, A
Cossio, J
Neuberger, JM
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1997, 27 (04) : 1041 - 1053
[32] On the Solution of the Dirichlet Problem with Rational Holomorphic Boundary Data
Peter Ebenfelt
Michael Viscardi
Computational Methods and Function Theory, 2006, 5 (2) : 445 - 457
[33] Solution to the Dirichlet Problem of the Wave Equation on a Star Graph
Arepova, Gaukhar
Alexeyeva, Ludmila
Arepova, Dana
MATHEMATICS, 2023, 11 (20)
[34] The Method of Integral Equations in the Mixed Dirichlet–Neumann Problem for the Laplace Equation in the Exterior of Cuts in the Plane
P. A. Krutitskii
A. I. Sgibnev
Differential Equations, 2001, 37 : 1363 - 1375
[35] Solution of the Dirichlet Problem with Polynomial Data for the Polyharmonic Equation in a Ball
Karachik, V. V.
DIFFERENTIAL EQUATIONS, 2015, 51 (08) : 1033 - 1042
[36] Solution of Dirichlet problem for a triangle region in terms of elliptic functions
Kurt, Nurcan
Sezer, Mehmet
APPLIED MATHEMATICS AND COMPUTATION, 2006, 182 (01) : 73 - 81
[37] Solution of the Dirichlet problem with polynomial data for the polyharmonic equation in a ball
V. V. Karachik
Differential Equations, 2015, 51 : 1033 - 1042
[38] Optimal Recovery of the Solution to the Dirichlet Problem in the Half-Plane
E. V. Abramova
E. O. Sivkova
Siberian Mathematical Journal, 2023, 64 : 507 - 513
[39] Asymptotics of the Dirichlet problem solution for a ring with quadratic growths on the boundaries
Tursunov, D. A.
Erkebaev, U. Z.
Tursunov, E. A.
IZVESTIYA INSTITUTA MATEMATIKI I INFORMATIKI-UDMURTSKOGO GOSUDARSTVENNOGO UNIVERSITETA, 2016, (02): : 73 - 81
[40] Optimal Recovery of the Solution to the Dirichlet Problem in the Half-Plane
Abramova, E. V.
Sivkova, E. O.
SIBERIAN MATHEMATICAL JOURNAL, 2023, 64 (03) : 507 - 513

← 1 2 3 4 5 →