Nonlinear potential theory and weighted Sobolev spaces / Bengt Ove Turesson.

Format:

Book

Author/Creator:

Turesson, Bengt Ove, 1961-

Series:

Lecture notes in mathematics (Springer-Verlag) ; 1736.

Lecture notes in mathematics, 0075-8434 ; 1736

Language:

English

Subjects (All):

Potential theory (Mathematics).

Nonlinear theories.

Sobolev spaces.

Physical Description:

xiv, 173 pages ; 24 cm.

Place of Publication:

Berlin ; New York : Springer, [2000]

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.

Notes:

Includes bibliographical references (pages [163]-170) and index.

ISBN:

3540675884

OCLC:

44084163