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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…mehr

Produktbeschreibung
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.
• Produktdetails
• Lecture Notes in Mathematics Vol.1736
• Verlag: Springer, Berlin
• 2000.
• Seitenzahl: 196
• Erscheinungstermin: 21. Juni 2000
• Deutsch, Englisch
• Abmessung: 235mm x 155mm x 10mm
• Gewicht: 331g
• ISBN-13: 9783540675884
• ISBN-10: 3540675884
• Artikelnr.: 09175201
Inhaltsangabe
Preliminaries.- Sobolev spaces.- Potential theory.- Applications of potential theory to Sobolev spaces.