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  • © 2000

Nonlinear Potential Theory and Weighted Sobolev Spaces

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
  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

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.

Keywords

  • Lemma
  • Potential theory
  • Sobolev space
  • Sobolev spaces
  • partial differential equation
  • partial differential equations

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, Differential Equations

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions