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- catalog abstract "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.".
- catalog contributor b11756469.
- catalog created "2000.".
- catalog date "2000".
- catalog date "2000.".
- catalog dateCopyrighted "2000.".
- catalog description "Includes bibliographical references.".
- catalog description "Introduction -- Preliminaries: Notation and conventions. Basic results concerning weights -- Sobolev spaces: The Sobolev space $W (mp) w (/Omega)$. The Sobolev space $W (mp) w (/Omega)$. Hausdorff measures. Isoperimetric inequalities. Some Sobolev type inequalities. Embeddings into L q µ(Û) -- Potential theory: Norm inequalities for fractional integrals and maximal functions. Meyers' Theory for Lp-capacities. Bessel and Riesz capacities. Hausdorff capacities. Variational capacities. Thinness: The case 1< p.".
- catalog description "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.".
- catalog extent "xiv, 173 p. ;".
- catalog identifier "3540675884 (softcover : alk. paper)".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1736.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1736".
- catalog issued "2000".
- catalog issued "2000.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "510 s 515/.9 21".
- catalog subject "Differential equations, partial.".
- catalog subject "Mathematics.".
- catalog subject "Nonlinear theories.".
- catalog subject "Potential theory (Mathematics)".
- catalog subject "QA3 .L28 no. 1736+ QA404.7".
- catalog subject "Sobolev spaces.".
- catalog tableOfContents "Introduction -- Preliminaries: Notation and conventions. Basic results concerning weights -- Sobolev spaces: The Sobolev space $W (mp) w (/Omega)$. The Sobolev space $W (mp) w (/Omega)$. Hausdorff measures. Isoperimetric inequalities. Some Sobolev type inequalities. Embeddings into L q µ(Û) -- Potential theory: Norm inequalities for fractional integrals and maximal functions. Meyers' Theory for Lp-capacities. Bessel and Riesz capacities. Hausdorff capacities. Variational capacities. Thinness: The case 1< p.".
- catalog title "Nonlinear potential theory and weighted Sobolev spaces / Bengt Ove Turesson.".
- catalog type "text".