I am having problems with the following question, any and all help is appreciated.
Suppose $\Delta u = 0$ in $D$
$\displaystyle\frac{du}{d\eta} +au = 0$ on $\partial D$ where $D$ is a bounded domain in $\mathbb{R}^3$ for which the divergence theorem holds, vector $\eta$ is a unit outward normal on $\partial D$ and $a >0$. Show that $u \equiv 0$.
I need help starting this though any help towards completing it would also be helpful. Thank you.