The Sobolev capacity on metric spaces

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Researchers

Research units

  • University of Helsinki

Abstract

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.

Details

Original languageEnglish
Pages (from-to)367-382
Number of pages16
JournalANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
Volume21
Issue number2
Publication statusPublished - 1996
MoE publication typeA1 Journal article-refereed

ID: 5434789