Suppose \(\Omega \subseteq \mathbb{R}^n\), \(x_0 \in \partial \Omega\). A function \(w \in C^0(\overline{\Omega})\) is called a barrier if:

1. \(w(x_0) = 0\),
2. \(w(x) > 0\) for all \(x \in \overline{\Omega} \setminus \{x_0\}\),
3. \(w\) is superharmonic .

Then \(x_0\) is called regular.

See also Link to heading

• outer sphere condition
• outer cone condition