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Book synopsis

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.

Book details

Book category Books in German Naturwissenschaften, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie, Stochastik, Mathematische

• Full title: Nonlinear Potential Theory and Weighted Sobolev Spaces
• Author: Bengt O. Turesson
• Language: German
• Binding: Paperback
• Number of pages: 180
• EAN: 9783540675884
• ISBN: 3540675884
• ID: 05275115
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Weight: 328 g
• Dimensions: 157 × 235 × 14 mm
• Date of publishing: 21. June 2000

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