A characterization of the orthogonal of Δ(H2(Ω) ∩ H10(Ω)) in L2(Ω)

Franck Assous; Patrick Ciarlet

doi:10.1016/S0764-4442(97)84769-6

A characterization of the orthogonal of Δ(H²(Ω) ∩ H¹₀(Ω)) in L²(Ω)

Titre traduit de la contribution: Une caractérisation de l'orthogonal de Δ(H²(Ω) ∩ H¹₀(Ω)) dans L²(Ω)

Franck Assous
, Patrick Ciarlet

CEA/LV

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

9 Citations (Scopus)

Résumé

In the case of a nonconvex polyhedral domain with a Lipschitz continuous boundary, we characterize, in L² (Ω), the orthogonal subspace of the image of H²(Ω) ∩ H¹₀(Ω) by the Laplace operator. Later on, this result will lead to a decomposition of the solution of Maxwell's equations into a regular term and a singular term. This Note is the first part of the extension of [1] to tridimensional domains.

Titre traduit de la contribution	Une caractérisation de l'orthogonal de Δ(H²(Ω) ∩ H¹₀(Ω)) dans L²(Ω)
langue originale	Anglais
Pages (de - à)	605-610
Nombre de pages	6
journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	325
Numéro de publication	6
Les DOIs	https://doi.org/10.1016/S0764-4442(97)84769-6
état	Publié - 1 janv. 1997
Modification externe	Oui

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10.1016/S0764-4442(97)84769-6

Contient cette citation

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AU - Ciarlet, Patrick

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N2 - In the case of a nonconvex polyhedral domain with a Lipschitz continuous boundary, we characterize, in L2 (Ω), the orthogonal subspace of the image of H2(Ω) ∩ H10(Ω) by the Laplace operator. Later on, this result will lead to a decomposition of the solution of Maxwell's equations into a regular term and a singular term. This Note is the first part of the extension of [1] to tridimensional domains.

AB - In the case of a nonconvex polyhedral domain with a Lipschitz continuous boundary, we characterize, in L2 (Ω), the orthogonal subspace of the image of H2(Ω) ∩ H10(Ω) by the Laplace operator. Later on, this result will lead to a decomposition of the solution of Maxwell's equations into a regular term and a singular term. This Note is the first part of the extension of [1] to tridimensional domains.

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A characterization of the orthogonal of Δ(H2(Ω) ∩ H10(Ω)) in L2(Ω)

Résumé

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Contient cette citation

A characterization of the orthogonal of Δ(H²(Ω) ∩ H¹₀(Ω)) in L²(Ω)