Nonlinear potential theory and weighted Sobolev spaces. (English) Zbl 0949.31006

Lecture Notes in Mathematics. 1736. Berlin: Springer. xiv, 173 p. (2000).
The aim of this Lecture Note is to show how a number of results from the theory of non-weighted Sobolev spaces and from non-weighted potential theory can be extended to the weighted context.
Almost all results are established for Muckenhoupt weights; a few results are shown to hold for more general classes of weights such as doubling weights.
The book is based on the Ph. D. thesis of the author and the results are due to himself.


31C45 Other generalizations (nonlinear potential theory, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
31-02 Research exposition (monographs, survey articles) pertaining to potential theory
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
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