Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
