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Full-Text Articles in Physical Sciences and Mathematics
The P -Royden And P -Harmonic Boundaries For Metric Measure Spaces, Marcello Lucia, Michael J. Puls
The P -Royden And P -Harmonic Boundaries For Metric Measure Spaces, Marcello Lucia, Michael J. Puls
Publications and Research
Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfy 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.
Graphs Of Bounded Degree And The P-Harmonic Boundary, Michael J. Puls
Graphs Of Bounded Degree And The P-Harmonic Boundary, Michael J. Puls
Publications and Research
Let p be a real number greater than one and let G be a connected graph of bounded degree. We introduce the p-harmonic boundary of G and use it to characterize the graphs G for which the constant functions are the only p-harmonic functions on G. We show that any continuous function on the p-harmonic boundary of G can be extended to a function that is p-harmonic on G. We also give some properties of this boundary that are preserved under rough-isometries. Now let Gamma be a finitely generated group. As an application of our results, we characterize the vanishing …