Sobolev spaces with zero boundary values on metric spaces

Authors
Kilpelainen, T Kinnunen, J Martio, O
Citation
T. Kilpelainen et al., Sobolev spaces with zero boundary values on metric spaces, POTENT ANAL, 12(3), 2000, pp. 233-247
Citations number
24
Categorie Soggetti
Mathematics
Journal title
POTENTIAL ANALYSIS
ISSN journal
09262601 → ACNP
Volume
12
Issue
3
Year of publication
2000
Pages
233 - 247
Database
ISI
SICI code
0926-2601(200005)12:3<233:SSWZBV>2.0.ZU;2-K
Abstract
We generalize the definition of the first order Sobolev spaces with zero bo undary values to an arbitrary metric space endowed with a Borel regular mea sure. We show that many classical results extend to the metric setting. The se include completeness, lattice properties and removable sets.