Let be a bounded open connected subset of with a Lipschitz-continuous boundary and let be a deformation of the set satisfying in . It is established that there exists a constant with the following property: for each deformation satisfying a.e. in , there exist an n×n rotation matrix and a vector in such that
Soit un ouvert borné connexe de à frontière lipschitzienne et soit une déformation de l'ensemble satisfaisant dans . On établit l'existence d'une constante ayant la propriété suivante : quelle que soit la déformation satisfaisant p.p. dans , il existe une matrice n×n de rotation et un vecteur tels que
Accepted:
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Philippe G. Ciarlet 1; Cristinel Mardare 2
@article{CRMATH_2004__338_6_505_0, author = {Philippe G. Ciarlet and Cristinel Mardare}, title = {An estimate of the {\protect\emph{H}\protect\textsuperscript{1}-norm} of deformations in terms of the {\protect\emph{L}\protect\textsuperscript{1}-norm} of their {Cauchy{\textendash}Green} tensors}, journal = {Comptes Rendus. Math\'ematique}, pages = {505--510}, publisher = {Elsevier}, volume = {338}, number = {6}, year = {2004}, doi = {10.1016/j.crma.2004.01.014}, language = {en}, }
TY - JOUR AU - Philippe G. Ciarlet AU - Cristinel Mardare TI - An estimate of the H1-norm of deformations in terms of the L1-norm of their Cauchy–Green tensors JO - Comptes Rendus. Mathématique PY - 2004 SP - 505 EP - 510 VL - 338 IS - 6 PB - Elsevier DO - 10.1016/j.crma.2004.01.014 LA - en ID - CRMATH_2004__338_6_505_0 ER -
%0 Journal Article %A Philippe G. Ciarlet %A Cristinel Mardare %T An estimate of the H1-norm of deformations in terms of the L1-norm of their Cauchy–Green tensors %J Comptes Rendus. Mathématique %D 2004 %P 505-510 %V 338 %N 6 %I Elsevier %R 10.1016/j.crma.2004.01.014 %G en %F CRMATH_2004__338_6_505_0
Philippe G. Ciarlet; Cristinel Mardare. An estimate of the H1-norm of deformations in terms of the L1-norm of their Cauchy–Green tensors. Comptes Rendus. Mathématique, Volume 338 (2004) no. 6, pp. 505-510. doi : 10.1016/j.crma.2004.01.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.01.014/
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