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Superposition operator in Sobolev spaces on domain

Labutin, Denis

Description

For an arbitrary open set Ω ⊂ ℝn we characterize all functions G on the real line such that G o u ∈ W1,p(Ω) for all u ∈ W1,p. New element in the proof is based on Maz'ya's capacitary criterion for the imbedding W1,p(Ω) → L∞(Ω).

dc.contributor.authorLabutin, Denis
dc.date.accessioned2015-12-13T23:20:46Z
dc.date.available2015-12-13T23:20:46Z
dc.identifier.issn0002-9939
dc.identifier.urihttp://hdl.handle.net/1885/90857
dc.description.abstractFor an arbitrary open set Ω ⊂ ℝn we characterize all functions G on the real line such that G o u ∈ W1,p(Ω) for all u ∈ W1,p. New element in the proof is based on Maz'ya's capacitary criterion for the imbedding W1,p(Ω) → L∞(Ω).
dc.publisherAmerican Mathematical Society
dc.sourceProceedings of the American Mathematical Society
dc.subjectKeywords: Sobolev spaces; Superposition operator
dc.titleSuperposition operator in Sobolev spaces on domain
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume128
dc.date.issued2000
local.identifier.absfor010105 - Group Theory and Generalisations
local.identifier.ariespublicationMigratedxPub21341
local.type.statusPublished Version
local.contributor.affiliationLabutin, Denis, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.issue2
local.bibliographicCitation.startpage3399
local.bibliographicCitation.lastpage3403
dc.date.updated2015-12-12T09:04:27Z
local.identifier.scopusID2-s2.0-23044521792
CollectionsANU Research Publications

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