Abstract and Applied Analysis
Volume 7 (2002), Issue 7, Pages 357-374

Strongly nonlinear potential theory on metric spaces

Noureddine Aïssaoui

École Normale Supérieure, B.P. 5206, Ben Souda, Fès, Morocco

Received 23 January 2002

Copyright © 2002 Noureddine Aïssaoui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.