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Nonlinear Potential Theory and Weighted Sobolev Spaces

Nonlinear Potential Theory and Weighted Sobolev Spaces

Brand
Springer Nature
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N/A
Part Number
0
GTIN
9783540451686
Condition
New
Product Description

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.

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