# Boundary conditions for pde

As i understand, the purpose of laplaces/poissons equation is to recast the question from a geometrical one to a differential equation.
im trying to figure out what are the appropriate boundary conditions for poissons equation:

where v is potential and p is the local charge density

Also, what method do i use to solve this equation? I cant remember a thing about pde's but i have some knowledge of ODE's. It appears linear Because V doesnt show up anywhere, and P is a function of x,y,z but I dont really know where to begin with this though.

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Simon Bridge
Note: we'd normally write: $$\nabla^2\phi = \frac{\rho_{free}}{\epsilon_0}$$ ... since this does not assume a specific coordinate system.