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Existence and regularity of positive solutions of a degenerate elliptic problem
Author(s) -
Guo ZongMing,
Guan XiaoHong,
Wan FangShu
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700352
Subject(s) - mathematics , degenerate energy levels , bounded function , dirichlet problem , pure mathematics , domain (mathematical analysis) , embedding , sobolev space , dirichlet distribution , mathematical analysis , boundary value problem , physics , quantum mechanics , artificial intelligence , computer science
Existence and regularity of positive solutions of a degenerate elliptic Dirichlet problem of the form − div ( a ( x ) ∇ u ) = b ( x ) u pin Ω, u = 0 on ∂ Ω , where Ω is a bounded smooth domain in R N , 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.