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On the compactness theorem for differential forms. (Russian, English) Zbl 1036.58002
Sib. Mat. Zh. 44, No. 1, 132-142 (2003); translation in Sib. Math. J. 44, No. 1, 107-115 (2003).
S. Kichenassamy [Commun. Pure Appl. Math. 42, 47–53 (1989; Zbl 0649.58002)] formulated sufficient conditions for compactness of the embedding of the space \(W_p^k\) of differential forms on a closed manifold into the space \( F_p^k \) of currents on this manifold in corresponding norms.
The authors of the paper under review extend this result to arbitrary Banach complexes, to spaces of differential forms on compact manifolds with boundary, and to elliptic differential complexes on closed manifolds. They find sufficient and necessary conditions for compactness of these embeddings.
MSC:
58A10 Differential forms in global analysis
58J10 Differential complexes
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