Nonlinear Potential Theory and Weighted Sobolev Spaces

  • Authors
  • Bengt Ove Turesson

Part of the Lecture Notes in Mathematics book series (LNM, volume 1736)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Bengt Ove Turesson
    Pages 1-14
  3. Bengt Ove Turesson
    Pages 15-68
  4. Bengt Ove Turesson
    Pages 69-140
  5. 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.


Lemma Potential theory Sobolev space Sobolev spaces partial differential equation

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-67588-4
  • Online ISBN 978-3-540-45168-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site