Nonlinear Potential Theory and Weighted Sobolev Spaces

Bengt Ove Turesson (auth.)3540675884, 9783540675884

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.

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Table of contents :
Preliminaries….Pages 1-14
Sobolev spaces….Pages 15-68
Potential theory….Pages 69-140
Applications of potential theory to Sobolev spaces….Pages 141-162