Open Access
21 August 2002 Strongly nonlinear potential theory on metric spaces
Noureddine Aïssaoui
Abstr. Appl. Anal. 7(7): 357-374 (21 August 2002). DOI: 10.1155/S1085337502203024


We define Orlicz-Sobolev spaces on an arbitrary metric space with a Borel regular outer measure, and we develop a capacity theory based on these spaces. We study basic properties of capacity and several convergence results. We prove that each Orlicz-Sobolev function has a quasi-continuous representative. We give estimates for the capacity of balls when the measure is doubling. Under additional regularity assumption on the measure, we establish some relations between capacity and Hausdorff measures.


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Noureddine Aïssaoui. "Strongly nonlinear potential theory on metric spaces." Abstr. Appl. Anal. 7 (7) 357 - 374, 21 August 2002.


Published: 21 August 2002
First available in Project Euclid: 14 April 2003

zbMATH: 1017.46022
MathSciNet: MR1939129
Digital Object Identifier: 10.1155/S1085337502203024

Primary: 31B15 , 46E35
Secondary: 28A80

Rights: Copyright © 2002 Hindawi

Vol.7 • No. 7 • 21 August 2002
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