Existence and regularity of positive solutions of a degenerate elliptic problem

ZongMing Guo, XiaoHong Guan and FangShu Wan

Mathematische Nachrichten, 2019, vol. 292, issue 1, 56-78

Abstract: Existence and regularity of positive solutions of a degenerate elliptic Dirichlet problem of the form −div(a(x)∇u)=b(x)up in Ω, u=0 on ∂Ω, where Ω is a bounded smooth domain in RN, N≥1, are obtained via new embeddings of some weighted Sobolev spaces with singular weights a(x) and b(x). It is seen that a(x) and b(x) admit many singular points in Ω. The main embedding results in this paper provide some generalizations of the well‐known Caffarelli–Kohn–Nirenberg inequality.

Date: 2019
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