Geodesic
The Hilbert-Schmidt Property for Embedding Maps between Sobolev Spaces
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1079-1084

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

Let H0 m(Ω) denote the so-called Sobolev space consisting of functions denned on a region Ω in n-dimensional Euclidean space, which together with their generalized derivatives of all orders ⩽m belong to , and which vanish in a certain sense on the boundary ∂Ω. (Precise definitions are given in the next section.) For each pair m, k of non-negative integers the inclusion H0m+k(Ω) ⊂ H0 m(Ω) defines a natural “embedding” map. For the case of a bounded region Ω it is well known that these maps are completely continuous, and even, for sufficiently large k, of Hilbert-Schmidt type. We have discussed complete continuity in the case of unbounded regions in an earlier paper; here we consider conditions on Ω which imply the Hilbert-Schmidt property for embeddings. 
Clark, Colin. The Hilbert-Schmidt Property for Embedding Maps between Sobolev Spaces. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1079-1084. doi: 10.4153/CJM-1966-107-1
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