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-Δ is Positive Definite on a "Spiny Urchin"

Published online by Cambridge University Press:  20 November 2018

Robert A. Adams
Robert A. Adams*
Affiliation:
University of British Columbia
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In a recent note [3] in this department C. Clark has shown that Rellich's theorem on the compactness of the imbedding is valid if G is the "spiny urchin" domain obtained by removing from the plane the union of the sets Sk (k = 1, 2,…) defined in polar coordinates by

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 2 , April 1969 , pp. 229 - 231
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Adams, R. A., The Rellich-Kondrachov theorem for unbounded domains. Archive Rat. Mech. Anal. 29 (1968) 390–394.Google Scholar
2. Adams, R. A., Compact imbedding theorems for quasibounded domains (to appear).Google Scholar
3. Clark, C. W., Rellich's embedding theorem for a "spiny urchin". Can. Math. Bull. 10 (1967) 731–734.Google Scholar