1. The Neumann problem for the Laplace equation on general domains
- Creator:
- Medková, Dagmar
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Laplace equation, Neumann problem, potential, and boundary integral equation method
- Language:
- English
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public