Essential norms and localization moduli of Sobolev embeddings for general domains | Zendy

Lang J. | Zendy; Maz'ya V. | Zendy

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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.

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