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New nonlinear estimates for surfaces in terms of their fundamental forms.

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Title: New nonlinear estimates for surfaces in terms of their fundamental forms.
Authors: Ciarlet, Philippe G.1 mapgc@cityu.edu.hk, Malin, Maria1 mmalin2-c@my.cityu.edu.hk, Mardare, Cristinel2 mardare@ann.jussieu.fr
Source: Comptes Rendus. Mathématique. Feb2017, Vol. 355 Issue 2, p226-231. 6p.
Subjects: Nonlinear analysis, Euclidean geometry, Algebraic spaces, Elastic plates & shells, Sobolev spaces
Abstract (English): We establish several estimates of the distance between two surfaces immersed in the three-dimensional Euclidean space in terms of the distance between their fundamental forms, measured in various Sobolev norms. These estimates, which can be seen as nonlinear versions of linear Korn inequalities on a surface appearing in the theory of linearly elastic shells, generalize in particular the nonlinear Korn inequality established in 2005 by P. G. Ciarlet, L. Gratie, and C. Mardare. [ABSTRACT FROM AUTHOR]
Abstract (French): Résumé Nous établissons plusieurs majorations de la distance entre deux surfaces immergées dans l'espace euclidien tridimensionnel en fonction de la distance entre leurs formes fondamentales, mesurée à l'aide de diverses normes de Sobolev. Ces estimations, qui peuvent être vues comme des versions non linéaires des inégalités de Korn linéaires sur une surface apparaissant dans la théorie de coques linéairement élastiques, généralisent en particulier l'inégalité de Korn non linéaire sur une surface établie en 2005 par P. G. Ciarlet, L. Gratie et C. Mardare. [ABSTRACT FROM AUTHOR]
Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: New nonlinear estimates for surfaces in terms of their fundamental forms.
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  Data: <searchLink fieldCode="AR" term="%22Ciarlet%2C+Philippe+G%2E%22">Ciarlet, Philippe G.</searchLink><relatesTo>1</relatesTo><i> mapgc@cityu.edu.hk</i><br /><searchLink fieldCode="AR" term="%22Malin%2C+Maria%22">Malin, Maria</searchLink><relatesTo>1</relatesTo><i> mmalin2-c@my.cityu.edu.hk</i><br /><searchLink fieldCode="AR" term="%22Mardare%2C+Cristinel%22">Mardare, Cristinel</searchLink><relatesTo>2</relatesTo><i> mardare@ann.jussieu.fr</i>
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  Data: <searchLink fieldCode="DE" term="%22Nonlinear+analysis%22">Nonlinear analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Euclidean+geometry%22">Euclidean geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+spaces%22">Algebraic spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Elastic+plates+%26+shells%22">Elastic plates & shells</searchLink><br /><searchLink fieldCode="DE" term="%22Sobolev+spaces%22">Sobolev spaces</searchLink>
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  Data: We establish several estimates of the distance between two surfaces immersed in the three-dimensional Euclidean space in terms of the distance between their fundamental forms, measured in various Sobolev norms. These estimates, which can be seen as nonlinear versions of linear Korn inequalities on a surface appearing in the theory of linearly elastic shells, generalize in particular the nonlinear Korn inequality established in 2005 by P. G. Ciarlet, L. Gratie, and C. Mardare. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label: Abstract (French)
  Group: Ab
  Data: Résumé Nous établissons plusieurs majorations de la distance entre deux surfaces immergées dans l'espace euclidien tridimensionnel en fonction de la distance entre leurs formes fondamentales, mesurée à l'aide de diverses normes de Sobolev. Ces estimations, qui peuvent être vues comme des versions non linéaires des inégalités de Korn linéaires sur une surface apparaissant dans la théorie de coques linéairement élastiques, généralisent en particulier l'inégalité de Korn non linéaire sur une surface établie en 2005 par P. G. Ciarlet, L. Gratie et C. Mardare. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.crma.2017.01.002
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        Text: English
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      – SubjectFull: Nonlinear analysis
        Type: general
      – SubjectFull: Euclidean geometry
        Type: general
      – SubjectFull: Algebraic spaces
        Type: general
      – SubjectFull: Elastic plates & shells
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      – SubjectFull: Sobolev spaces
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              Text: Feb2017
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