Embeddings of weighted Sobolev spaces and degenerate elliptic problems.

New embeddings of some weighted Sobolev spaces with weights a( x) and b( x) are established. The weights a( x) and b( x) can be singular. Some applications of these embeddings to a class of degenerate elliptic problems of the form −div( a( x)∇ u) = b( x) f( x, u) in Ω, u = 0 on ∂Ω, where Ω is a bounded or unbounded domain in R, N > 2, are presented. The main results of this paper also give some generalizations of the well-known Caffarelli-Kohn-Nirenberg inequality. [ABSTRACT FROM AUTHOR]