Laplace operator in half sphere space

Question

The laplace operator is defined for the sphere as : \begin{equation} \frac{\partial^2 f}{\partial r^2} +\frac{2}{r} \frac{\partial f}{\partial r} +\frac{1}{r^2\sin\theta} \frac{\partial }{\partial \theta}\left( \sin\theta\frac{\partial f}{\partial \theta} \right) +\frac{1}{r^2\sin^2\theta}\frac{\partial^2 f}{\partial \varphi^2} \end{equation} Is it possible to have a definition for an half sphere space ?