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The \(p\)-Royden and \(p\)-harmonic boundaries for metric measure spaces. (English) Zbl 1317.31021

Summary: Let \(p\) be a real number greater than one and let \(X\) be a locally compact, noncompact metric measure space that satisfies certain conditions. The \(p\)-Royden and \(p\)-harmonic boundaries of \(X\) are constructed by using the \(p\)-Royden algebra of functions on \(X\) and a Dirichlet type problem is solved for the \(p\)-Royden boundary. We also characterize the metric measure spaces whose \(p\)-harmonic boundary is empty.

MSC:

31E05 Potential theory on fractals and metric spaces
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
30L99 Analysis on metric spaces
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References:

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