Say we want to calculate the gravitational potential everywhere around(outside) a solid, circular, right cylinder. We want to use Poisson's equation for gravity for that (Laplace(U) = -4*pi*density or something like that). Since we want to know the potential outside the cyllinder this reduces to laplaces equation laplace(U) = 0
My question is: What would the boundary conditions for this equation be? Obviously one is that it decays to zero at infinity, but what about the boundary conditions on surface of the cyllinder?