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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.

Potential theory (Mathematics) --- Nonlinear theories --- Sobolev spaces --- Espaces de Sobolev --- Niet-lineaire theorieën --- Potentiaaltheorie --- Potentiel [Théorie du ] --- Ruimten van Sobolev --- Sobolev [Espaces de ] --- Sobolev [Ruimten van ] --- Spaces [Sobolev ] --- Theorieën [Niet-lineaire ] --- Théories non-linéaires --- Potential theory (Mathematics). --- Partial differential equations. --- Potential Theory. --- Partial Differential Equations. --- Partial differential equations --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics