Solve
in the first quadrant with on the boundaries in 2 dimensions.
Now I know the solution to this problem for the half-plane is determined by the fact that
where
and
which leads to
So to solve this problem, however, I think I need to add more image sources, so at a guess I would have...
and then due to superposition, Green's function would be given by
or something to that effect. Am I on the right track with this?