Boundary conditions for Laplace's equation

IFNT · Feb 3, 2011

I don't seem to grasp the meaning of boundary conditions for Laplace's equation.

Consider the Lagendre expansion of the potential at x due to a unit charge 1/|x-x'|, where x' is the position of the unit point charge.
To do the expansion, we need to consider a volume in space where the potential satisfies the Laplace equation. I can see that the potential satisfies Laplaces equation anywhere in space except at x=x', but what are the boundary conditions? Don't we have to know the potential at x=x', which is a boundary?

IFNT · Feb 4, 2011

Am I too vague in my question?

Boundary conditions for Laplace's equation

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Boundary conditions for Laplace's equation

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