Existence and regularity of positive solutions of a degenerate elliptic problem

Abstract

AbstractExistence and regularity of positive solutions of a degenerate elliptic Dirichlet problem of the form in Ω, on , where Ω is a bounded smooth domain in , , are obtained via new embeddings of some weighted Sobolev spaces with singular weights and . It is seen that and admit many singular points in Ω. The main embedding results in this paper provide some generalizations of the well‐known Caffarelli–Kohn–Nirenberg inequality.