= Exterior cone condition
An open set satisfies an exterior cone condition at $z$ if a solid cone with vertex $z$ lies outside the set in some neighbourhood of $z$. The stronger global version requires the closures of the cone and the set to meet only at $z$. In two dimensions, a <power barrier for an exterior cone> makes such a point a <regular boundary point> for the <Dirichlet problem>. Local cone conditions suffice for local boundary regularity; a global cone is an additional geometric assumption.
Back to article page
