Sobolev Spaces on Riemannian Manifolds

Emmanuel Hebey (auth.)3540617221, 9783540617228

Several books deal with Sobolev spaces on open subsets of R (n), but none yet with Sobolev spaces on Riemannian manifolds, despite the fact that the theory of Sobolev spaces on Riemannian manifolds already goes back about 20 years. The book of Emmanuel Hebey will fill this gap, and become a necessary reading for all using Sobolev spaces on Riemannian manifolds.
Hebey’s presentation is very detailed, and includes the most recent developments due mainly to the author himself and to Hebey-Vaugon. He makes numerous things more precise, and discusses the hypotheses to test whether they can be weakened, and also presents new results.

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Table of contents :
Geometric preliminaries….Pages 1-9
Sobolev spaces….Pages 10-16
Sobolev embeddings….Pages 17-57
The best constants problems….Pages 58-89
Sobolev spaces in the presence of symmetries….Pages 90-105