The Sobolev capacity on metric spaces

Juha Kinnunen*, Olli Martio

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

97 Citations (Scopus)


We develop a capacity theory based on the definition of Sobolev functions on metric spaces with a Borel regular outer measure. Basic properties of capacity, including monotonicity, countable subadditivity and several convergence results, are studied. As an application we prove that each Sobolev function has a quasicontinuous representative. For doubling measures we provide sharp estimates for the capacity of balls. Capacity and Hausdorff measures are related under an additional regularity assumption on the measure.

Original languageEnglish
Pages (from-to)367-382
Number of pages16
Issue number2
Publication statusPublished - 1996
MoE publication typeA1 Journal article-refereed

Fingerprint Dive into the research topics of 'The Sobolev capacity on metric spaces'. Together they form a unique fingerprint.

Cite this