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)

Translated title of the contribution: A characterization of the orthogonal of Δ(H²(Ω) ∩ H¹₀(Ω)) in L²(Ω)

Franck Assous
, Patrick Ciarlet

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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.

Translated title of the contribution	A characterization of the orthogonal of Δ(H²(Ω) ∩ H¹₀(Ω)) in L²(Ω)
Original language	English
Pages (from-to)	605-610
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	325
Issue number	6
DOIs	https://doi.org/10.1016/S0764-4442(97)84769-6
State	Published - Sep 1997
Externally published	Yes

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10.1016/S0764-4442(97)84769-6

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abstract = "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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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)

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