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A First Course in Sobolev Spaces

Giovanni Leoni
Publisher: 
American Mathematical Society
Publication Date: 
2017
Number of Pages: 
734
Format: 
Hardcover
Edition: 
2
Series: 
Graduate Studies in Mathematics 181
Price: 
94.00
ISBN: 
9781470429218
Category: 
Monograph
[Reviewed by
Fernando Q. Gouvêa
, on
11/20/2017
]

See our review of the first edition. The author's new preface points to many changes in the second edition. In the first part of the book, he has generalized the theory from real-valued functions to functions taking values in a Banach space. There is a new chapter on the Bochner integral and a new section on interpolation inequalities for Sobolev functions of one variable. As before, the first half of the book is meant as "a textbook for an advanced undergraduate course or beginning graduate course in real analysis or functions of one variable."

The second part of the book is aimed at more advanced readers, and it too has seen many revisions. In particular, the author says that he has "caved in and decided to include higher order derivatives," which allows him to include results that were not in the first edition.

 

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Fernando Q. Gouvêa is the editor of MAA Reviews.

See the table of contents in the publisher's webpage.