[Nouvelles estimations pour des surfaces en fonction de leurs formes fondamentales]
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.
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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@article{CRMATH_2017__355_2_226_0,
author = {Ciarlet, Philippe G. and Malin, Maria and Mardare, Cristinel},
title = {New nonlinear estimates for surfaces in terms of their fundamental forms},
journal = {Comptes Rendus. Math\'ematique},
pages = {226--231},
publisher = {Elsevier},
volume = {355},
number = {2},
year = {2017},
doi = {10.1016/j.crma.2017.01.002},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.01.002/}
}
TY - JOUR AU - Ciarlet, Philippe G. AU - Malin, Maria AU - Mardare, Cristinel TI - New nonlinear estimates for surfaces in terms of their fundamental forms JO - Comptes Rendus. Mathématique PY - 2017 SP - 226 EP - 231 VL - 355 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.01.002/ DO - 10.1016/j.crma.2017.01.002 LA - en ID - CRMATH_2017__355_2_226_0 ER -
%0 Journal Article %A Ciarlet, Philippe G. %A Malin, Maria %A Mardare, Cristinel %T New nonlinear estimates for surfaces in terms of their fundamental forms %J Comptes Rendus. Mathématique %D 2017 %P 226-231 %V 355 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.01.002/ %R 10.1016/j.crma.2017.01.002 %G en %F CRMATH_2017__355_2_226_0
Ciarlet, Philippe G.; Malin, Maria; Mardare, Cristinel. New nonlinear estimates for surfaces in terms of their fundamental forms. Comptes Rendus. Mathématique, Tome 355 (2017) no. 2, pp. 226-231. doi : 10.1016/j.crma.2017.01.002. http://www.numdam.org/articles/10.1016/j.crma.2017.01.002/
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