New nonlinear estimates for surfaces in terms of their fundamental forms

Philippe G. Ciarlet; Maria Malin; Cristinel Mardare

doi:10.1016/j.crma.2017.01.002

New nonlinear estimates for surfaces in terms of their fundamental forms

Philippe G. Ciarlet, Maria Malin, Cristinel Mardare

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

9 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	226-231
Journal	Comptes Rendus Mathematique
Volume	355
Issue number	2
Online published	1 Feb 2017
DOIs	https://doi.org/10.1016/j.crma.2017.01.002
Publication status	Published - Feb 2017

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title = "New nonlinear estimates for surfaces in terms of their fundamental forms",

abstract = "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.",

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language = "English",

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T1 - New nonlinear estimates for surfaces in terms of their fundamental forms

AU - Ciarlet, Philippe G.

AU - Malin, Maria

AU - Mardare, Cristinel

PY - 2017/2

Y1 - 2017/2

N2 - 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.

AB - 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.

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U2 - 10.1016/j.crma.2017.01.002

DO - 10.1016/j.crma.2017.01.002

M3 - RGC 21 - Publication in refereed journal

SN - 1631-073X

VL - 355

SP - 226

EP - 231

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 2

ER -

New nonlinear estimates for surfaces in terms of their fundamental forms

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New nonlinear estimates for surfaces in terms of their fundamental forms

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