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Nonlinear Potential Theory and Weighted Sobolev Spaces

 Taschenbuch
Besorgungstitel | Lieferzeit:3-5 Tage I
ISBN-13:
9783540675884
Einband:
Taschenbuch
Seiten:
180
Autor:
Bengt O. Turesson
Gewicht:
331 g
Format:
236x158x11 mm
Serie:
Vol.1736, Lecture Notes in Mathematics
Sprache:
Deutsch
Beschreibung:

Preliminaries.- Sobolev spaces.- Potential theory.- Applications of potential theory to Sobolev spaces.
This book systematically develops the nonlinear potential theory connected with the weighted Sobolev space Wm,pw( ), 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 Poincare 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, Poincare inequalities, and spectral synthesis theorems.

Preliminaries.- Sobolev spaces.- Potential theory.- Applications of potential theory to Sobolev spaces.
This book systematically develops the nonlinear potential theory connected with the weighted Sobolev space Wm,pw( ), 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 Poincare 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, Poincare inequalities, and spectral synthesis theorems.
Autor: Bengt O. Turesson
ISBN-13:: 9783540675884
ISBN: 3540675884
Verlag: Springer, Berlin
Gewicht: 331g
Seiten: 180
Sprache: Deutsch
Sonstiges: Taschenbuch, 236x158x11 mm, XII, 180 p.