Definition:Barrier

Definition
A complex function $\varphi \in \C \left({\overline \Omega}\right)$ is a barrier for $\Omega$ at $z \in \partial \Omega$ :
 * $\varphi$ is subharmonic
 * $\varphi ( z ) = 0$
 * $\varphi < 0$ on $\partial \Omega \setminus \{ z \}$

We call the boundary point $z \in \partial \Omega$ regular if there is a barrier for $\Omega$ at $z \in \partial \Omega$.