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 Poincare 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, Poincare inequalities, and spectral synthesis theorems.
- ISBN10 3662165732
- ISBN13 9783662165737
- Publish Date 15 January 2014 (first published 21 June 2000)
- Publish Status Withdrawn
- Out of Print 18 October 2014
- Publish Country US
- Imprint Springer
- Format Paperback (US Trade)
- Pages 194
- Language English