Geodesic
A Compact Imbedding Theorem for Functions without Compact Support
Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 305-309

Voir la notice de l'article provenant de la source Cambridge University Press

The extension of the Rellich-Kondrachov theorem on the complete continuity of Sobolev space imbeddings of the sort 1 to unbounded domains G has recently been under study [1–5] and this study has yielded [4] a condition on G which is necessary and sufficient for the compactness of (1). Similar compactness theorems for the imbeddings 2 are well known for bounded domains G with suitably regular boundaries, and the question naturally arises whether any extensions to unbounded domains can be made in this case. 
Adams, R. A.; Fournier, John. A Compact Imbedding Theorem for Functions without Compact Support. Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 305-309. doi: 10.4153/CMB-1971-056-2
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[1] 1. Adams, R. A., Compact Sobolev imbeddings for unbounded domains, Pacific J. Math. 32 (1970), 1-7. Google Scholar

[2] 2. Adams, R. A., The Rellich Kondrachov theorem for unbounded domains, Arch. Rational Mech. Anal. 29 (1968), 390-394. Google Scholar

[3] 3. Adams, R. A., Compact imbedding theorems for quasibounded domains, Trans. Amer. Math. Soc. 148 (1970), 445-459. Google Scholar

[4] 4. Adams, R. A., Capacity and compact imbeddings, J. Math. Mech. 19 (1970), 923-929. Google Scholar

[5] 5. Clark, C. W., An embedding theorem for function spaces, Pacific J. Math. 19 (1966), 243-251. Google Scholar

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