Geodesic
Some Imbedding Theorems for Sobolev Spaces
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 517-530

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

We shall be concerned throughout this paper with the Sobolev space Wm,p (G) and the existence and compactness (or lack of it) of its imbeddings (i.e. continuous inclusions) into various LP spaces over G, where G is an open, not necessarily bounded subset of n-dimensional Euclidean space En . For each positive integer m and each real p ≧ 1 the space Wm,p (G) consists of all u in LP (G) whose distributional partial derivatives of all orders up to and including m are also in LP (G). With respect to the norm 1.1 Wm,p (G) is a Banach space. It has been shown by Meyers and Serrin [9] that the set of functions in Cm (G) which, together with their partial derivatives of orders up to and including m, are in LP (G) forms a dense subspace of Wm,p (G). 
Adams, R. A.; Fournier, John. Some Imbedding Theorems for Sobolev Spaces. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 517-530. doi: 10.4153/CJM-1971-055-3
@article{10_4153_CJM_1971_055_3,
     author = {Adams, R. A. and Fournier, John},
     title = {Some {Imbedding} {Theorems} for {Sobolev} {Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {517--530},
     year = {1971},
     volume = {23},
     number = {3},
     doi = {10.4153/CJM-1971-055-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-055-3/}
}
TY  - JOUR
AU  - Adams, R. A.
AU  - Fournier, John
TI  - Some Imbedding Theorems for Sobolev Spaces
JO  - Canadian journal of mathematics
PY  - 1971
SP  - 517
EP  - 530
VL  - 23
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-055-3/
DO  - 10.4153/CJM-1971-055-3
ID  - 10_4153_CJM_1971_055_3
ER  - 
%0 Journal Article
%A Adams, R. A.
%A Fournier, John
%T Some Imbedding Theorems for Sobolev Spaces
%J Canadian journal of mathematics
%D 1971
%P 517-530
%V 23
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-055-3/
%R 10.4153/CJM-1971-055-3
%F 10_4153_CJM_1971_055_3

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

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

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

[4] 4. Adams, R. A. and Fournier, J., A compact imbedding theorem for functions without compact support (to appear in Can. Math. Bull.). Google Scholar

[5] 5. Adams, R. D., Aronszajn, N., and Smith, K. T., Theory of Bessel potentials, Part II, Ann. Inst. Fourier (Grenoble), 17 (1967), 1–135. Google Scholar

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

[7] 7. Gagliardo, E., Propriété di alcune classi difunzioni in piu variabili, Ricerche Mat. 7 (1958), 102–137. Google Scholar

[8] 8. Kondrachov, V. I., Certain properties of functions in the spaces D>, Dokl. Akad. NaukSSSR, 48 (1955), 563–566. ,+Dokl.+Akad.+NaukSSSR,+48+(1955),+563–566.>Google Scholar

[9] 9. Meyers, N. G. and Serrin, J., H = W, Proc. Nat. Acad. Sci. U.S.A., 51 (1964), 1055–1056. Google Scholar

[10] 10. Rellich, F., Ein Satz über mittlere Konvergenz, Gö;ttingen Nachr. (1930), 30–35. Google Scholar

Cité par Sources :