p-调和函数关于Mazurkiewicz边界的狄利克雷问题
The Dirichlet problem for p-harmonic functions with respect to the Mazurkiewicz boundary
摘要：
在本文中，我们发展了Perron方法来解决p-Laplacian的模拟，即p-调和函数，与Mazurkiewicz边界值的狄利克雷问题。这里考虑的设置是度量空间，其中讨论的域的边界被替换为Mazurkiewicz边界。Sobolev和连续函数的分辨性，以及小集合上扰动的不变性结果。我们使用这些结果，以改善已知的解析度和标准（度量）边界上的函数的不变性结果。我们还通过讨论几个例子来说明本文的结果。
英文摘要：
In this paper we develop the Perron method for solving the Dirichlet problem for the analog of the p-Laplacian, i.e. for p-harmonic functions, with Mazurkiewicz boundary values. The setting considered here is that of metric spaces, where the boundary of the domain in question is replaced with the Mazurkiewicz boundary. Resolutivity for Sobolev and continuous functions, as well as invariance results for perturbations on small sets, are obtained. We use these results to improve the known resolutivity and invariance results for functions on the standard (metric) boundary. We also illustrate the results of this paper by discussing several examples.
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