We say that $\Omega$ is a strongly star shaped domain (with respect to $0$ for example) in $\mathbb R ^n$ if:

$$\Omega = \{x\in \mathbb R ^n : \left \| x \right \| < g(\frac{x}{\left \| x\right \|})\} $$ and $$\partial \Omega = \{x\in \mathbb R ^n : \left \| x \right \| = g(\frac{x}{\left \| x \right \|})\} $$ with $g$ is a continuous, positive function on the unit sphere.

In this paper,
Bramble uses the fact that : **Any Lipschitz domain can be written as the union of strongly star shaped Lipschitz domains: $\Omega=\cup_{i=1}^{M}\Omega_i$**

Can you help me to find why do we have this result? Do you have any references in which I can find this proposition?

*PS: Sorry to ask this question again, but this did not get answered (as I had desired) on M.SE.*