Consider the subset $\Omega\subset\mathbf{R}^n$, $\Omega=\{x=(x_1,...,x_n)\in\mathbf{R}^n;x_n>\varphi(x_1,...,x_n)\},$ where $\varphi$ is a Lipschitz continuous function, that is, $\Omega$ is a unbounded set, bounded for a Lipschitz graph.
Why this set satisfies the interior sphere condtion?
Interior sphere condition means that for each $z\in\partial\Omega$, there is a ball $B_r(\xi)$ satisfying $\partial B_r(\xi)\cap\overline\Omega=\{z\}$.