A density result in Sobolev spaces

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4 Citations (Scopus)

Abstract

We prove, for 1 ≤ p < ∞ and Ω a polygonal or regular open subset of ℝN, the density in W1,p(Ω) of a set of regular functions satisfying a homogeneous Neumann condition on the boundary of Ω. We also give applications of this result and a generalization to mixed Dirichlet-Neumann boundary conditions.

Original languageEnglish
Pages (from-to)697-714
Number of pages18
JournalJournal des Mathematiques Pures et Appliquees
Volume81
Issue number7
DOIs
Publication statusPublished - 12 Aug 2002
Externally publishedYes

Cite this

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title = "A density result in Sobolev spaces",
abstract = "We prove, for 1 ≤ p < ∞ and Ω a polygonal or regular open subset of ℝN, the density in W1,p(Ω) of a set of regular functions satisfying a homogeneous Neumann condition on the boundary of Ω. We also give applications of this result and a generalization to mixed Dirichlet-Neumann boundary conditions.",
author = "J{\'e}r{\^o}me Droniou",
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journal = "Journal des Mathematiques Pures et Appliquees",
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A density result in Sobolev spaces. / Droniou, Jérôme.

In: Journal des Mathematiques Pures et Appliquees, Vol. 81, No. 7, 12.08.2002, p. 697-714.

Research output: Contribution to journalArticleResearchpeer-review

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AB - We prove, for 1 ≤ p < ∞ and Ω a polygonal or regular open subset of ℝN, the density in W1,p(Ω) of a set of regular functions satisfying a homogeneous Neumann condition on the boundary of Ω. We also give applications of this result and a generalization to mixed Dirichlet-Neumann boundary conditions.

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