Sobolev spaces on Riemannian manifolds

Bibliographic Information

Sobolev spaces on Riemannian manifolds

Emmanuel Hebey

(Lecture notes in mathematics, 1635)

Springer, c1996

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Note

Includes bibliographical references (p. [106]-113), and notation and subject indexes

Description and Table of Contents

Description

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.

Table of Contents

Geometric preliminaries.- Sobolev spaces.- Sobolev embeddings.- The best constants problems.- Sobolev spaces in the presence of symmetries.

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