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.
@article{bwmeta1.element.doi-10_1515_agms-2015-0008,
author = {Marcello Lucia and Michael J. Puls},
title = {The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces},
journal = {Analysis and Geometry in Metric Spaces},
volume = {3},
year = {2015},
zbl = {1317.31021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0008}
}
Marcello Lucia; Michael J. Puls. The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces. Analysis and Geometry in Metric Spaces, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0008/
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