
Preface  Preview Material  Table of Contents  Supplementary Material 
Graduate Studies in Mathematics 2009; 607 pp; hardcover Volume: 105 ISBN10: 0821847686 ISBN13: 9780821847688 List Price: US$85 Member Price: US$68 Order Code: GSM/105 See also: A Basic Course in Partial Differential Equations  Qing Han Lectures on Elliptic and Parabolic Equations in Sobolev Spaces  N V Krylov Measure Theory and Integration  Michael E Taylor  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 onevariable 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. Request an examination or desk copy. Readership Graduate students and research mathematicians interested in Sobolev spaces, particularly their applications to PDEs. 


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