# Laplace equation with specific boundary conditions

How we can solve Laplace equation in the empty space $$z\ge0$$ for $$V(\vec{r})$$ with the given boundary conditions: it goes to zero at infinity and it is zero on the plane $$z=0$$ except inside a square centered in the origin with sides length $$a$$ and parallel to the $$x$$ and $$y$$ axis.

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