I'm studying Green functions on a ball (that I call $G$). I know that this function is harmonic, and that all their partial derivatives are harmonic (a consequence of representation formula).
Can I say that the directional derivative $$\frac{\partial G}{\partial \eta}$$ is harmonic? ($\eta$ is the outward unitary vector of the ball). I think it's true, but I'm not sure.
Thanks a lot,