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Publication list for Leoni, Giovanni

  • A First Course in Sobolev Spaces: Second Edition
    Base Product Code Keyword List: gsm; GSM; gsm/181; GSM/181; gsm-181; GSM-181
    Print Product Code: GSM/181
    Online Product Code: GSM/181.E
    Title (HTML): A First Course in Sobolev Spaces: Second Edition
    Author(s) (Product display): Giovanni Leoni
    Affiliation(s) (HTML): Carnegie Mellon University, Pittsburgh, PA
    Abstract:

    This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue–Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces.

    The second part of the book studies functions of several variables. It begins with an overview of classical results such as Rademacher's and Stepanoff's differentiability theorems, Whitney's extension theorem, Brouwer's fixed point theorem, and the divergence theorem for Lipschitz domains. It then moves to distributions, Fourier transforms and tempered distributions.

    The remaining chapters are a treatise on Sobolev functions. The second edition focuses more on higher order derivatives and it includes the interpolation theorems of Gagliardo and Nirenberg. It studies embedding theorems, extension domains, chain rule, superposition, Poincaré's inequalities and traces.

    A major change compared to the first edition is the chapter on Besov spaces, which are now treated using interpolation theory.

    Book Series Name: Graduate Studies in Mathematics
    Volume: 181
    Publication Month and Year: 2017-11-02
    Copyright Year: 2017
    Page Count: 734
    Cover Type: Hardcover
    Print ISBN-13: 978-1-4704-2921-8
    Online ISBN 13: 978-1-4704-4226-2
    Print ISSN: 1065-7339
    Online ISSN: 1065-7339
    Primary MSC: 46
    Secondary MSC: 26; 30
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    SXG Subject: AA
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    Online Price 1: 94.00
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    Online Price 2 Label: AMS Member
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    Print Add to Cart URL: /some/url/at/AMS/GSM-181
    Electronic Add to Cart URL: /some/url/at/AMS/GSM-181.E
    Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4226-2&pisbn=978-1-4704-2921-8&epc=GSM/181.E&ppc=GSM/181&title=A%20First%20Course%20in%20Sobolev%20Spaces%3A%20Second%20Edition&author=Giovanni%20Leoni&type=DE
    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4226-2&pisbn=978-1-4704-2921-8&epc=GSM/181.E&ppc=GSM/181&title=A%20First%20Course%20in%20Sobolev%20Spaces%3A%20Second%20Edition&author=Giovanni%20Leoni&type=R
    Readership:

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

    Related Products: Lectures on Linear Partial Differential Equations An Introduction to Lie Groups and the Geometry of Homogeneous Spaces Introduction to Representation Theory
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  • A First Course in Sobolev Spaces
    Base Product Code Keyword List: gsm; GSM; gsm/105; GSM/105; gsm-105; GSM-105
    Print Product Code: GSM/105
    Online Product Code: GSM/105.E
    Title (HTML): A First Course in Sobolev Spaces
    Author(s) (Product display): Giovanni Leoni
    Affiliation(s) (HTML): Carnegie Mellon University, Pittsburgh, PA
    Abstract:

    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.

    Book Series Name: Graduate Studies in Mathematics
    Volume: 105
    Publication Month and Year: 2009-07-15
    Copyright Year: 2009
    Page Count: 607
    Cover Type: Hardcover
    Print ISBN-13: 978-0-8218-4768-8
    Online ISBN 13: 978-1-4704-1169-5
    Print ISSN: 1065-7339
    Online ISSN: 1065-7339
    Primary MSC: 46
    Secondary MSC: 26
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    SXG Subject: AN; DE
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/gsm-105
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    Dual Price 2: 89
    Print Add to Cart URL: /some/url/at/AMS/GSM-105
    Electronic Add to Cart URL: /some/url/at/AMS/GSM-105.E
    Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1169-5&pisbn=978-0-8218-4768-8&epc=GSM/105.E&ppc=GSM/105&title=A%20First%20Course%20in%20Sobolev%20Spaces&author=Giovanni%20Leoni&type=DE
    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1169-5&pisbn=978-0-8218-4768-8&epc=GSM/105.E&ppc=GSM/105&title=A%20First%20Course%20in%20Sobolev%20Spaces&author=Giovanni%20Leoni&type=R
    Readership:

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

    Related Products: A Basic Course in Partial Differential Equations Lectures on Elliptic and Parabolic Equations in Sobolev Spaces Measure Theory and Integration