The Mixed Problem for the Laplace Equation in an Exterior Domain with an Arbitrary Partition of the Boundary

被引：0

作者：

P. A. Krutitskii

机构：

[1] M. V. Lomonosov Moscow State University,Russian Academy of Sciences

[2] M. V. Keldysh Institute of Applied Mathematics,undefined

来源：

Mathematical Notes | 2001年 / 69卷

关键词：

mixed boundary-value problem; Laplace equation; arbitrary partition of boundary; Dirichlet condition; Fredholm integral equation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper we propose a method for solving the mixed boundary-value problem for the Laplace equation in a connected exterior domain with an arbitrary partition of the boundary. All simple closed curves making up the boundary are divided into three sets. On the elements of the first set the Dirichlet condition is given, on the elements of the second set the third boundary condition is prescribed, and the third set, in turn, is divided into two subsets of simple closed arcs, with the Dirichlet condition prescribed on the elements of one of these subsets and the third boundary condition on the elements of the other subset. The problem is reduced to a uniquely solvable Fredholm equation of the second kind in a Banach space. The third boundary-value problem and the mixed Dirichlet--Neumann problem are particular cases of the problem under study.

引用

页码：799 / 813

页数：14

共 13 条

[1]

Krutitskii P. A.(1996)On the mixed problem for the Helmholtz equation in a multiply connected domain Zh. Vychisl. Mat. i Mat. Fiz. 36 127-137

[2]

Krutitskii P. A.(1996)The mixed problem for the Helmholtz equation outside cuts in the planes Differentsial'nye Uravneniya 32 1153-1162

[3]

Krutitskii P. A.(1997)The mixed problem for the Laplace equation outside cuts in the plane Differentsial'nye Uravneniya 33 1181-1190

[4]

Homentcovschi D.(1987)On the Dirichlet-Neumann mixed boundary-value problem for harmonic functions in plane multiply connected domains Rev. Romaine Math. Pures Appl. 32 801-810

[5]

Krutitskii P. A.(1996)Fast stratified flow over several obstacles, including wings IMA J. Appl. Math. 57 243-256

[6]

Krutitskii P. A.(1997)The 2-D Neumann problem in an exterior domain bounded by closed and open curves Math. Methods Appl. Sci. 20 1551-1562

[7]

Krutitskii P. A.(1998)Wave propagation in a 2-D exterior domain bounded by closed and open curves Nonlinear Analysis, Theory, Methods, and Applications 32 135-144

[8]

Krutitskii P. A.(1998)The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves Internat. J. Math. Math. Sci. 21 209-216

[9]

Krutitskii P. A.(1998)The Dirichlet problem for the dissipative Helmholtz equation in a plane domain bounded by closed and open curves Hiroshima Math. J. 28 149-168

[10]

Krutitskii P. A.(1996)The second initial boundary value problem for the gravitational-gyroscopic wave equation in exterior domains Mat. Zametki 60 40-57

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