Calculus of Variations and Geometric Measure Theory
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G. Leoni

A First Course in Sobolev Spaces

created by leoni on 29 Aug 2009



Inserted: 29 aug 2009

Journal: Graduate Studies in Mathematics, American Mathematical Society
Volume: 105
Pages: 607
Year: 2009

Webpage: http:/www.ams.orgbookstore-getitemitem=gsm-105


About the book: Sobolev spaces are a fundamental tool in the modern study of partial differential equations. In this book, Leoni takes a novel approach to the theory by looking at Sobolev spaces as the natural development of monotone, absolutely continuous, and BV functions of one variable. In this way, the majority of the text can be read without the prerequisite of a course in functional analysis. The first part of this text is devoted to studying functions of one variable. Several of the topics treated occur in courses on real analysis or measure theory. Here, the perspective emphasizes their applications to Sobolev functions, giving a very different flavor to the treatment. This elementary start to the book makes it suitable for advanced undergraduates or beginning graduate students. Moreover, the one-variable part of the book helps to develop a solid background that facilitates the reading and understanding of Sobolev functions of several variables.

The second part of the book is more classical, although it also contains some recent results. Besides the standard results on Sobolev functions, this part of the book includes chapters on BV functions, symmetric rearrangement, and Besov spaces.

The book contains over 200 exercises.


Graduate students and research mathematicians interested in Sobolev spaces, particularly their applications to PDEs.

The AMS is hosting a webpage for this book at


where updates, corrections, and other material may be found.

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