The trichotomy between regular, semiregular, and strongly irregular boundary points for \(p\)-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a \(p\)-Poincaré inequality, \(1<p<\infty \). We show that these are local properties. We also deduce several characterizations of semiregular points and strongly irregular points. In particular, semiregular points are characterized by means of capacity, \(p\)-harmonic measures, removability, and semibarriers.

中文翻译：

---

度量空间中无界集上 p 调和函数的半正则和强不规则边界点

对于完全度量空间中的无界开集，使用支持\(p\) -Poincaré 不等式的加倍测度获得\(p\) -调和函数的正则、半正则和强不规则边界点之间的三分法，\(1< p<\infty \)。我们证明这些是本地属性。我们还推导出了半规则点和强不规则点的几个特征。特别是，半规则点的特征在于容量、\(p\)-谐波测量、可移除性和半势垒。