Customer Reviews

Sobolev Spaces, Volume 140, Second Edition (Pure and Applied Mathematics)

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As a PhD student in mathematics focusing on theoretical PDE, I find this monograph to be one of the most useful in my collect. The book is self contained and very easy to read, requiring only a background in real analysis at the beginning graduate/senior undergrad level. This text covers a wide range of topics from the basics of topological vector spaces, all the way through interpolation methods and Besov spaces, but maintains a deep enough level so that most researchers will find this book to be very useful as a reference for the subject. In particular, I really like the completeness by which the imbedding theorems in the book are stated and proved. In addition to the content, the book is also beautifully bound and is printed on very high quality paper.

I highly recommend this book. It is a valuable reference and a great introduction to sobolev spaces for people interested in functional analysis.

A very interesting textbook for people interested in functional analysis. It provides a great introduction for beginners but also clear and rigorous demonstrations of more technical points.

A comprehensive exposition of the Sobolev creation: the ethos of the solutions for differential equations. Ethos means dwelling, but much more than abode it means a way of being. The Sobolev spaces are the whole being of the solutions, the way they are. The way they look like.

Adams and Fournier present that ethos with detail. All important and essential properties are studied rigorously and exhaustively. Those dwellings have the convenient property of being complete. This means that they are Euclidean extensions without gaps; they are continuous extensions, no holes, no hiatus. One cannot gain everything, there is always something missing. The lack of the ethos created by Sobolev is huge: the metric limitation does not guarantee scarceness of extension. This is a major problem we have to deal with. A new concept of proximity has to be invented. Also, it is very important to enable reification since a solution living in the Sobolev ethos has to be a vintage solution.

The book is indispensable for graduate student and researcher that wish to struggle along the road of the non-linear differential equations.