Solution of the Poisson Equation: General Boundary Conditions

The discussion of the solution of the Poisson equation is slightly more involved, if more general boundary conditions are considered. The boundary value problems named after Dirichlet as well as the one named after von Neumann will be introduced in this chapter. The two boundary value problems differ in the sense, that in the first case values for the potential on (metallic) surfaces are specified, in the second problem one specifies the values for the normal derivative of the potential (the electric field).