An open set \(\Omega \subset \mathbb{R}^d\) satisfies the outer cone condition if and only if for every boundary point \(x\in \partial \Omega\) there is a cone \(K\) such that \(K\cap \overline{\Omega}=\{x\}\).

Remarks
  • If \(x_0 \in \partial \Omega\) satisfies the outer cone condition, then \(x\) is regular .