Abstract and Applied Analysis

Strongly nonlinear potential theory on metric spaces

Noureddine Aïssaoui

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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.

Article information

Abstr. Appl. Anal., Volume 7, Number 7 (2002), 357-374.

First available in Project Euclid: 14 April 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 31B15: Potentials and capacities, extremal length
Secondary: 28A80: Fractals [See also 37Fxx]


Aïssaoui, Noureddine. Strongly nonlinear potential theory on metric spaces. Abstr. Appl. Anal. 7 (2002), no. 7, 357--374. doi:10.1155/S1085337502203024. https://projecteuclid.org/euclid.aaa/1050348397

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