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Compactness of Embeddings of Sobolev Spaces
Author(s) -
Duc Duong Minh
Publication year - 1989
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/s2-40.1.105
Subject(s) - compact space , embedding , mathematics , sobolev space , sobolev inequality , boundary (topology) , pure mathematics , domain (mathematical analysis) , birnbaum–orlicz space , inequality , interpolation space , mathematical analysis , functional analysis , computer science , artificial intelligence , biochemistry , chemistry , gene
We prove a Poincaré inequality for functions vanishing on a part of the boundary of their domain. Using this inequality we study the compactness of embedding of weighted Sobolev spaces. Some concrete examples are given.