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

• Autorzy: Marcello Lucia , Michael J. Puls
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Dirichlet problem at infinity; metric measure space; p-harmonic function; p-parabolic; p-Royden algebra; p-weak upper gradient; (p, p)-Sobolev inequality

Kategorie tematyczne

• 54E45: Compact (locally compact) metric spaces
• 31B20: Boundary value and inverse problems
• 31C25: Dirichlet spaces

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-01-23

zaakceptowano

2015-05-05

online

2015-06-01

Twórcy

autor

Marcello Lucia

• Department of Mathematics, College of Staten Island-CUNY, 2800 Victory Boulevard, Staten Island, NY 10314, USA

autor

Michael J. Puls

• Department of Mathematics, John Jay College-CUNY, 524 West 59th Street, New York, NY 10019, USA

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Identyfikatory

DOI

10.1515/agms-2015-0008