Nonlinear potential theory and weighted Sobolev spaces /

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Bibliographic Details
Author / Creator:	Turesson, Bengt Ove, 1961-
Imprint:	Berlin ; New York : Springer, ©2000.
Description:	1 online resource (xiv, 173 pages).
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 1736 Lecture notes in mathematics (Springer-Verlag) ; 1736.
Subject:	Potential theory (Mathematics) Nonlinear theories. Sobolev spaces. Nonlinear theories. Potential theory (Mathematics) Sobolev spaces.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11065884

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ISBN:	9783540451686 3540451684 3540675884 9783540675884
Notes:	Includes bibliographical references (pages 163-170) and index.
Summary:	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 Poincar 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, Poincar inequalities, and spectral synthesis theorems.
Other form:	Print version: Turesson, Bengt Ove, 1961- Nonlinear potential theory and weighted Sobolev spaces. Berlin ; New York : Springer, ©2000 3540675884
Standard no.:	10.1007/BFb0103908

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