How to show the following statement?

Let $\Omega$ be a bounded

Lipschitzconvexdomain. If $u$ satisfies the following equation,$$ -\Delta u - k^2 u = f \quad\mbox{ in }\Omega \\ \nabla u \cdot n + i k u = g \quad\mbox{ on }\partial \Omega $$

Then the following estimate holds:

$$ |u|_{H^2(\Omega)} \leq C \left(\Vert f+k^2 u \Vert_{0,\Omega} + \Vert\nabla u \cdot n\Vert_{\frac{1}{2},\partial \Omega}\right). $$

Thank you for any hint on this.

**Remark:**

- This statement is quoted from a thesis On generalized finite element methods by Jens Markus Melenk on P.121. It says using regularity theory for '$-\Delta$' to get the statement.
- I made a mistake. The requirement for $\Omega$ should be bounded convex, not bounded Lipschitz.