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To do this, I'm trying to solve the differential equation [itex]\Delta V = 0[/itex] (harmonic). Together with the boundary condition [itex]V(R) = c[/itex].

From the null laplacian, one can obtain [itex]V(r) = -\dfrac{\alpha}{r} + \beta[/itex], but I'm lacking one boundary condition. Can this method be applied even when there's a singularity (i.e. [itex]V(0) = \infty[/itex])?

How does one solve this problem? What additional boundary conditions are there?