The Sobolev Capacity on Metric Spaces
Year: 1996
Type: article
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 mono- tonicity, 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.
Source: Annales Fennici Mathematici
Authors: Juha Kinnunen, Олли Мартио
Institution: University of Helsinki
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W147682785