The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces

• Main Authors: Lucia Marcello, Puls Michael J.
• Format: Article
• Language: English
• Published: De Gruyter 2015-06-01
• Series: Analysis and Geometry in Metric Spaces
• Subjects: dirichlet problem at infinity; metric measure space; p-harmonic function; p-parabolic; p-royden algebra; p-weak upper gradient; (p, p)-sobolev inequality; primary: 31b20; secondary: 31c25, 54e45
• Online Access: https://doi.org/10.1515/agms-2015-0008
• ISSN: 2299-3274

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.