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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
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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

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