Poisson's equation is: . This implicitly uses the cross product of the electric field is 0. Questions:

• method of solution in general boundary conditions
• Uniqueness of solution

Boundary conditions are given by on some surface (dirichlet boundary conditions), or on some surface (neumann problems).

Using green's theorem, you get for , 2 different solutions. This means uniqueness up to a constant for neumann boundary conditions and uniqueness for the dirichlet problem.

source psfile jl@crush.caltech.edu index spherical_coordinate_green_function greens_theorem green_function