Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-14T23:11:09.744Z Has data issue: false hasContentIssue false
  • English
  • Français

Properties of Equivalent Capacities

Published online by Cambridge University Press:  20 November 2018

R. A. Adams
R. A. Adams*
Affiliation:
University of British Columbia, VancouverBritish Columbia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Various definitions of capacity of a subset of a domain in Euclidean space have been used in recent times to shed light on the solvability and spectral theory of elliptic partial differential equations and to establish properties of the Sobolev spaces in which these equations are studied. In this paper we consider two definitions of the capacity of a closed set E in a domain G. One of these capacities measures, roughly speaking, the amount by which the set of function in C∞(G) which vanish near E fails to be dense in the Sobolev space Wm, p(G).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 5 - 11
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Adams, R. A., Capacity and compact imbeddings, J. Math. Mech. 19 (1970), 923-929.Google Scholar
2. Adams, R. A., Compact imbeddings of weighted Sobolev spaces on unbounded domains, J. Differential Equations, (to appear).Google Scholar
3. Calderon, A. P., Lebesgue spaces ofdifferentiate functions and distributions, Proc. Symposia Pure Math., Vol. IV, Amer. Math. Soc. (1961), 33-50.Google Scholar
4. Kondrat'ev, V. A., Solvability of the first boundary-value problem for strongly elliptic equations, Trans. Moscow Math. Soc. 16 (1967), 315-341.Google Scholar
5. Maz'ja, V. G., Polyharmonic capacity in the theory of the first boundary-value problem, (Russian), Sibirsk Mat. 1. 6 (1965), 127-148.Google Scholar