Abstract The theory of boundary regularity for p-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a p-Poincaré inequality, 1 < p < ∞. The barrier classification of regular boundary points is established, and it is shown that regularity is a local property of the boundary. We also obtain boundary regularity results for solutions of the obstacle problem on open sets, and characterize regularity further in several other ways.

中文翻译：

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度量空间中无界集上p-谐波函数的边界正则性和障碍问题的解

摘要 p-调和函数的边界正则性理论被扩展到完全度量空间中的无界开集，其加倍测度支持 p-Poincaré 不等式，1 < p < ∞。建立了规则边界点的障碍分类，表明规则性是边界的局部性质。我们还获得了开放集上障碍问题解决方案的边界正则性结果，并以其他几种方式进一步表征了正则性。