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Gossez's approximation theorems in Musielak–Orlicz–Sobolev spaces

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dc.abstract.enWe prove the density of smooth functions in the modular topology in Musielak–Orlicz–Sobolev spaces essentially extending the results of Gossez [17] obtained in the Orlicz–Sobolev setting. We impose new systematic regularity assumption on M which allows to study the problem of density unifying and improving the known results in Orlicz–Sobolev spaces, as well as variable exponent Sobolev spaces. We confirm the precision of the method by showing the lack of the Lavrentiev phenomenon in the double-phase case. Indeed, we get the modular approximation of functions by smooth functions in the double-phase space governed by the modular function with excluding the Lavrentiev phenomenon within the sharp range . See [11, Theorem 4.1] for the sharpness of the result.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorChlebicka, Iwona
dc.contributor.authorYoussfi, Ahmed
dc.contributor.authorAhmida, Youssef
dc.contributor.authorGwiazda, Piotr
dc.date.accessioned2024-01-25T02:22:09Z
dc.date.available2024-01-25T02:22:09Z
dc.date.issued2018
dc.description.financeNie dotyczy
dc.description.number9
dc.description.volume275
dc.identifier.doi10.1016/J.JFA.2018.05.015
dc.identifier.issn0022-1236
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/108064
dc.identifier.weblinkhttps://www.sciencedirect.com/science/article/pii/S002212361830199X
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofJournal of Functional Analysis
dc.relation.pages2538-2571
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enDensity of smooth functions
dc.subject.enThe Lavrentiev phenomenon
dc.subject.enThe Musielak–Orlicz–Sobolev spaces
dc.titleGossez's approximation theorems in Musielak–Orlicz–Sobolev spaces
dc.typeJournalArticle
dspace.entity.typePublication