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Weighted Sobolev Interpolation Inequalities on Certain Domains
Author(s) -
Chua SengKee
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/51.3.532
Subject(s) - mathematics , lipschitz continuity , interpolation (computer graphics) , sobolev inequality , inequality , sobolev space , pure mathematics , type (biology) , lipschitz domain , mathematical analysis , computer science , image (mathematics) , artificial intelligence , geology , paleontology
We obtain some weighted Sobolev interpolation inequalities on certain domains that include Lipschitz domains for doubling weights satisfying a weighted Poincaré inequality. These generalize most results in Gutierrez and Wheeden's paper [ 20 ]. We also give some applications on Lipschitz domains for weights of type dist (·, G ) 8 , where G ⊂ ∂.