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|a 9783540451686
|9 978-3-540-45168-6
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|a 10.1007/BFb0103908
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|a 515.96
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|a Turesson, Bengt O.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a Nonlinear Potential Theory and Weighted Sobolev Spaces
|h [electronic resource] /
|c by Bengt O. Turesson.
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|a 1st ed. 2000.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg :
|b Imprint: Springer,
|c 2000.
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|a XII, 180 p.
|b online resource.
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|a text
|b txt
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|a computer
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|a online resource
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|a text file
|b PDF
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1736
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|a 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.
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|a 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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|a Potential theory (Mathematics).
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|a Partial differential equations.
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|a Potential Theory.
|0 http://scigraph.springernature.com/things/product-market-codes/M12163
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|a Partial Differential Equations.
|0 http://scigraph.springernature.com/things/product-market-codes/M12155
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783540675884
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|i Printed edition:
|z 9783662165737
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1736
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|u https://doi.org/10.1007/BFb0103908
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a ZDB-2-LNM
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|a ZDB-2-BAE
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|a Mathematics and Statistics (Springer-11649)
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