Geodesic
The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

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.
Mots-clés : Dirichlet problem at infinity, metric measure space, p-harmonic function, p-parabolic, p-Royden algebra, p-weak upper gradient, (p, p)-Sobolev inequality 
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     author = {Lucia, Marcello and Puls, Michael J.},
     title = {The {p-Royden} and {p-Harmonic} {Boundaries} for {Metric} {Measure} {Spaces}},
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Lucia, Marcello; Puls, Michael J. The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a13/