[Potentiels vecteurs et scalaires, théorème de Poincaré et inégalité de Korn]
Dans cette Note, nous présentons plusieurs résultats concernant les potentiels vecteurs et les potentiels scalaires dans des domaines bornés tridimensionnels, éventuellement multiplement connexes. En particulier, on considère des potentiels singuliers correspondant à des données dans des espaces de Sobolev d'exposant négatif. On donne également des applications au théorème de Poincaré et à l'inégalité de Korn.
In this Note, we present several results concerning vector potentials and scalar potentials in a bounded, not necessarily simply-connected, three-dimensional domain. In particular, we consider singular potentials corresponding to data in negative order Sobolev spaces. We also give some applications to Poincaré's theorem and to Korn's inequality.
Publié le :
@article{CRMATH_2007__345_11_603_0,
author = {Amrouche, Ch\'erif and Ciarlet, Philippe G. and Ciarlet, Patrick Jr.},
title = {Vector and scalar potentials, {Poincar\'e's} theorem and {Korn's} inequality},
journal = {Comptes Rendus. Math\'ematique},
pages = {603--608},
publisher = {Elsevier},
volume = {345},
number = {11},
year = {2007},
doi = {10.1016/j.crma.2007.10.020},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.10.020/}
}
TY - JOUR AU - Amrouche, Chérif AU - Ciarlet, Philippe G. AU - Ciarlet, Patrick Jr. TI - Vector and scalar potentials, Poincaré's theorem and Korn's inequality JO - Comptes Rendus. Mathématique PY - 2007 SP - 603 EP - 608 VL - 345 IS - 11 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.10.020/ DO - 10.1016/j.crma.2007.10.020 LA - en ID - CRMATH_2007__345_11_603_0 ER -
%0 Journal Article %A Amrouche, Chérif %A Ciarlet, Philippe G. %A Ciarlet, Patrick Jr. %T Vector and scalar potentials, Poincaré's theorem and Korn's inequality %J Comptes Rendus. Mathématique %D 2007 %P 603-608 %V 345 %N 11 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.10.020/ %R 10.1016/j.crma.2007.10.020 %G en %F CRMATH_2007__345_11_603_0
Amrouche, Chérif; Ciarlet, Philippe G.; Ciarlet, Patrick Jr. Vector and scalar potentials, Poincaré's theorem and Korn's inequality. Comptes Rendus. Mathématique, Tome 345 (2007) no. 11, pp. 603-608. doi : 10.1016/j.crma.2007.10.020. http://archive.numdam.org/articles/10.1016/j.crma.2007.10.020/
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