Rellich′s Embedding Theorem for a “Spiny Urchin”

Colin Clark

doi:10.4153/CMB-1967-075-6

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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.

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

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Adams, Robert A 1968. Compact Sobolev imbeddings for unbounded domains with discrete boundaries. Journal of Mathematical Analysis and Applications, Vol. 24, Issue. 2, p. 326.

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Adams, Robert A. 1969. -Δ is Positive Definite on a "Spiny Urchin". Canadian Mathematical Bulletin, Vol. 12, Issue. 2, p. 229.

Adams, Robert A. 1970. Compact imbedding theorems for quasibounded domains. Transactions of the American Mathematical Society, Vol. 148, Issue. 2, p. 445.

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GEISINGER, LEANDER and WEIDL, TIMO 2011. SHARP SPECTRAL ESTIMATES IN DOMAINS OF INFINITE VOLUME. Reviews in Mathematical Physics, Vol. 23, Issue. 06, p. 615.

Kajikiya, Ryuji 2025. Sobolev compact embeddings in unbounded domains and its applications to elliptic equations. Journal of Mathematical Analysis and Applications, Vol. 543, Issue. 2, p. 129001.

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Rellich′s Embedding Theorem for a “Spiny Urchin”

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