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Weakly Differentiable Functions

Sobolev Spaces and Functions of Bounded Variation

  • Textbook
  • © 1989

Overview

Authors:
  1. William P. Ziemer

    1. Department of Mathematics, Indiana University, Bloomington, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 120)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Preliminaries

    • William P. Ziemer
    Pages 1-41

  3. Sobolev Spaces and Their Basic Properties

    • William P. Ziemer
    Pages 42-111

  4. Pointwise Behavior of Sobolev Functions

    • William P. Ziemer
    Pages 112-176

  5. Poincaré Inequalities—A Unified Approach

    • William P. Ziemer
    Pages 177-219

  6. Functions of Bounded Variation

    • William P. Ziemer
    Pages 220-282

  7. Back Matter

    Pages 283-310
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Keywords

About this book

The term "weakly differentiable functions" in the title refers to those inte­ n grable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed) measures with finite total variation. The former class of functions comprises what is now known as Sobolev spaces, though its origin, traceable to the early 1900s, predates the contributions by Sobolev. Both classes of functions, Sobolev spaces and the space of functions of bounded variation (BV func­ tions), have undergone considerable development during the past 20 years. From this development a rather complete theory has emerged and thus has provided the main impetus for the writing of this book. Since these classes of functions play a significant role in many fields, such as approximation theory, calculus of variations, partial differential equations, and non-linear potential theory, it is hoped that this monograph will be of assistance to a wide range of graduate students and researchers in these and perhaps other related areas. Some of the material in Chapters 1-4 has been presented in a graduate course at Indiana University during the 1987-88 academic year, and I am indebted to the students and colleagues in attendance for their helpful comments and suggestions.

Authors and Affiliations

  • Department of Mathematics, Indiana University, Bloomington, USA

    William P. Ziemer

Bibliographic Information

  • Book Title: Weakly Differentiable Functions

  • Book Subtitle: Sobolev Spaces and Functions of Bounded Variation

  • Authors: William P. Ziemer

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1015-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1989

  • Hardcover ISBN: 978-0-387-97017-2Published: 18 September 1989

  • Softcover ISBN: 978-1-4612-6985-4Published: 03 October 2012

  • eBook ISBN: 978-1-4612-1015-3Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XVI, 308

  • Topics: Potential Theory

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