The Neumann problem for the Laplace equation on general domains

Title:

The Neumann problem for the Laplace equation on general domains

Creator:

Medková, Dagmar

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:6b2df66a-4ada-4055-ae8b-9548882901ea
uuid:6b2df66a-4ada-4055-ae8b-9548882901ea

Subject:

Laplace equation, Neumann problem, potential, and boundary integral equation method

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 $\partial G$. 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1107-1139

Source:

Czechoslovak Mathematical Journal | 2007 Volume:57 | Number:4

Harvested from:

CDK

Metadata only:

false