Why does the Green's function $G(r,r_0)$ of the Laplace's equation $\nabla^2 u=0$, the domain being the half plane, is equal $0$ on the boundary? How can I interpret the Laplace's equation physically? Is there a way to intuitively interpret the Green's function in general?
Based on @Matt's comment, I am guessing that it is not generally true that the Green's function is 0 on the boundary?