Characterization of the kernel of the operator CURL CURL

Philippe G. Ciarlet; Patrick Ciarlet; Giuseppe Geymonat; Françoise Krasucki

doi:10.1016/j.crma.2007.01.001

Characterization of the kernel of the operator CURL CURL

Philippe G. Ciarlet
, Patrick Ciarlet
, Giuseppe Geymonat
, Françoise Krasucki

City University of Hong Kong
Université Montpellier-II

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

21 Citations (Scopus)

Abstract

In a simply-connected domain Ω in R³, the kernel of the operator CURL CURL acting on symmetric matrix fields from L_s² (Ω) to H_s^-2 (Ω) coincides with the space of linearized strain tensor fields. For not simply-connected domains, Volterra has characterized this kernel for smooth fields. Here we extend this result for domains with a Lipschitz-continuous boundary for fields in L_s² (Ω). To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

Original language	English
Pages (from-to)	305-308
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	344
Issue number	5
DOIs	https://doi.org/10.1016/j.crma.2007.01.001
Publication status	Published - 1 Mar 2007

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title = "Characterization of the kernel of the operator CURL CURL",

abstract = "In a simply-connected domain Ω in R3, the kernel of the operator CURL CURL acting on symmetric matrix fields from Ls2 (Ω) to Hs-2 (Ω) coincides with the space of linearized strain tensor fields. For not simply-connected domains, Volterra has characterized this kernel for smooth fields. Here we extend this result for domains with a Lipschitz-continuous boundary for fields in Ls2 (Ω). To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).",

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AU - Ciarlet, Philippe G.

AU - Ciarlet, Patrick

AU - Geymonat, Giuseppe

AU - Krasucki, Françoise

PY - 2007/3/1

Y1 - 2007/3/1

N2 - In a simply-connected domain Ω in R3, the kernel of the operator CURL CURL acting on symmetric matrix fields from Ls2 (Ω) to Hs-2 (Ω) coincides with the space of linearized strain tensor fields. For not simply-connected domains, Volterra has characterized this kernel for smooth fields. Here we extend this result for domains with a Lipschitz-continuous boundary for fields in Ls2 (Ω). To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

AB - In a simply-connected domain Ω in R3, the kernel of the operator CURL CURL acting on symmetric matrix fields from Ls2 (Ω) to Hs-2 (Ω) coincides with the space of linearized strain tensor fields. For not simply-connected domains, Volterra has characterized this kernel for smooth fields. Here we extend this result for domains with a Lipschitz-continuous boundary for fields in Ls2 (Ω). To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

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DO - 10.1016/j.crma.2007.01.001

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SP - 305

EP - 308

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 5

ER -

Characterization of the kernel of the operator CURL CURL

Abstract

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