The Sobolev capacity on metric spaces

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

Organisaatiot

  • University of Helsinki

Kuvaus

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.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut367-382
Sivumäärä16
JulkaisuANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
Vuosikerta21
Numero2
TilaJulkaistu - 1996
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 5434789