The Neumann problem for the Laplace equation on general domains

被引：0

作者：

Dagmar Medková

机构：

[1] Institute of Mathematics of the Academy of Sciences of the Czech Republic,

来源：

Czechoslovak Mathematical Journal | 2007年 / 57卷

关键词：

Laplace equation; Neumann problem; potential; boundary; integral equation method;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set G in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on ∂G. If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on G a necessary and sufficient condition for the solvability of the problem is given and the solution is constructed.

引用

页码：1107 / 1139

页数：32

共 12 条

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