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Nonlinear Potential Theory and Weighted Sobolev Spaces

  • Book
  • © 2000

Overview

Authors:
  1. Bengt Ove Turesson
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1736)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Preliminaries

    • Bengt Ove Turesson
    Pages 1-14

  3. Sobolev spaces

    • Bengt Ove Turesson
    Pages 15-68

  4. Potential theory

    • Bengt Ove Turesson
    Pages 69-140

  5. Applications of potential theory to Sobolev spaces

    • Bengt Ove Turesson
    Pages 141-162

  6. Back Matter

    Pages 163-173
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Keywords

About this book

The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.

Bibliographic Information

  • Book Title: Nonlinear Potential Theory and Weighted Sobolev Spaces

  • Authors: Bengt Ove Turesson

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0103908

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Softcover ISBN: 978-3-540-67588-4Published: 21 June 2000

  • eBook ISBN: 978-3-540-45168-6Published: 06 May 2007

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 180

  • Topics: Potential Theory, Partial Differential Equations

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