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Rellich′s Embedding Theorem for a “Spiny Urchin”

Published online by Cambridge University Press:  20 November 2018

Colin Clark
Colin Clark*
Affiliation:
University of British Columbia
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From the plane R2 we remove the union of the sets Sk (k = 1, 2, …) defined as follows (using the notation z = x + iy):

Sk = {z: arg z = nπ2-k for some integer n; |z|≥k}.

The remaining connected open set Ω we call the spiny urchin.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 5 , December 1967 , pp. 731 - 734
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Clark, C., An embedding theorem for function spaces. Pacific J. Math. 19 (1966), Z43-251.Google Scholar
2. Clark, C., Some embedding theorems for Sobolev spaces defined over unbounded domains, (to appear).Google Scholar
3. Rellich, F., EinSatz liber mittlere Konvergenz, Gottinger Nachr. (1933), 30-35.Google Scholar