Premium
Essential norms and localization moduli of Sobolev embeddings for general domains
Author(s) -
Lang J.,
Maz'ya V.
Publication year - 2008
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/jdn035
Subject(s) - mathematics , bounded function , sobolev space , embedding , pure mathematics , norm (philosophy) , compact space , moduli , boundary (topology) , operator (biology) , mathematical analysis , physics , computer science , biochemistry , chemistry , repressor , quantum mechanics , artificial intelligence , political science , transcription factor , law , gene
We introduce new measures of non‐compactness for the embedding operator E p , q (Ω): L p 1 (Ω) → L q (Ω) and describe their relations with the essential norm of E p, q (Ω), ‘local’ isoperimetric and isocapacitary constants. An explicit formula for the essential norm of E p, q (Ω) is obtained for domains with a power cusp on the boundary and bounded C 1 domains. The Neumann problem for a particular Schrödinger operator is discussed on domains with a power cusp.