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portada Nonlinear Potential Theory and Weighted Sobolev Spaces (Lecture Notes in Mathematics)
Type
Physical Book
Publisher
Author
Year
2000
Language
English
Pages
202
Format
Paperback
ISBN
3540675884
ISBN13
9783540675884
Edition No.
2000
Categories

Nonlinear Potential Theory and Weighted Sobolev Spaces (Lecture Notes in Mathematics)

Bengt Ove Turesson (Author) · Springer · Paperback

Nonlinear Potential Theory and Weighted Sobolev Spaces (Lecture Notes in Mathematics) - Bengt Ove Turesson

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Synopsis "Nonlinear Potential Theory and Weighted Sobolev Spaces (Lecture Notes in Mathematics) "

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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