Sturdy harmonic functions constitute all but the least tractable of the positive harmonic functions in potential-theoretic settings. They are the uniform limits on compact sets of positive, bounded harmonic functions and are also produced by a simple integral representation on the boundary of a natural compactification of the space on which they are defined. The boundary of that compactification is metrizable, and more regular for the Dirichlet problem, in general, than is the Martin boundary if that boundary is even defined in the setting.
Positivity – Springer Journals
Published: Oct 17, 2004
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