[Lecture Notes in Mathematics] Nonlinear Potential Theory and Weighted Sobolev Spaces Volume 1736 || Applications of potential theory to Sobolev spaces

✍ Scribed by Turesson, Bengt Ove

• Book ID: 127074826
• Publisher: Springer Berlin Heidelberg
• Year: 2000
• Tongue: English
• Weight: 912 KB
• Edition: 1
• Category: Article
• ISBN: 3540451684
• DOI: 10.1007/bfb0103912

✦ Synopsis

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 Poincaré 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, Poincaré inequalities, and spectral synthesis theorems.