Harmonic functions with conditions on $u$, $\frac{\partial u}{\partial n}$ on the boundary

Question

Let $\Omega$ be an open and bounded domain with boundary $\partial\Omega_1 \cup \partial\Omega_2 = \partial\Omega$.

Does there exist a $C^2$-function $u$ such that

$$ \begin{cases} \Delta u = 0 & \text{ in } \Omega, \\ u = 0, & \text{ on } \partial \Omega_1 \\ \frac{\partial u}{\partial n}= h>0 & \text{ on } \partial \Omega_2?\end{cases} $$