Abstract and Applied Analysis
Volume 7 (2002), Issue 7, Pages 357-374
Strongly nonlinear potential theory on metric spaces
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.