On the properties of solutions of the harmonic Dirichlet problem in a two-dimensional domain with cuts

被引：0

作者：

P. A. Krutitskii

机构：

[1] Moscow State University,

来源：

Differential Equations | 2010年 / 46卷

关键词：

Weak Solution; Dirichlet Problem; Classical Solution; Laplace Equation; Singular Integral Equation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider the Dirichlet problem for the Laplace equation in a plane domain with smooth cuts of arbitrary form for the case in which the solution is not continuous at the endpoints of the cuts. We present a well-posed statement of the problem, prove the existence and uniqueness theorems for the classical solution, obtain an integral representation of the solution, and use it to analyze the properties of the solution. We show that, as a rule, the Dirichlet problem in this setting has no weak solutions, even though there exists a classical solution.

引用

页码：1287 / 1298

页数：11

共 6 条

[1]

Krutitskii P.A.(2000)The Integral Representation for a Solution of the 2D Dirichlet Problem with Boundary Data on Closed and Open Curves Mathematika 47 339-354

[2]

Krutitskii P.A.(2000)The Dirichlet Problem for the 2D Laplace Equation in a Multiply Connected Domain with Cuts Proc. Edinb. Math. Soc. 43 325-341

[3]

Krutitskii P.A.(1998)The 2D Dirichlet Problem in an Exterior Domain with Cuts Z. Anal. Anwendungen 17 361-378

[4]

Krutitskii P.A.(1997)A Mixed Problem for the Laplace Equation Outside Cuts on the Plane Differ. Uravn. 33 1181-1190

[5]

Krutitskii P.A.(2005)The Mixed Problem in an Exterior Cracked Domain with Dirichlet Condition on Cracks Comput. Math. Appl. 50 769-782

[6]

Krutitskii P.A.(1994)The Dirichlet Problem for the Helmholtz Equation in the Exterior of Cuts in the Plane Zh. Vychisl. Mat. Mat. Fiz. 34 1237-1257

← 1 →