[Une équation elliptique fortement dégénérée provenant des équations de Maxwell semilinéaires.]
On étudie une équation nonlinéaire provenant d'une perturbation semilinéaire des équations de Maxwell. La présence du rotationnel rend l'équation fortement dégénérée. On propose une nouvelle approche liée à la décomposition de Hodge du potentiel vecteur A.
We study a nonlinear equation arising from a semilinear perturbation of the Maxwell equations. The presence of the curl operator makes this equation strongly degenerate. A new variational approach, related to the Hodge decomposition of the vector potential A, is developed.
Publié le :
@article{CRMATH_2004__339_12_839_0,
author = {Benci, Vieri and Fortunato, Donato},
title = {A strongly degenerate elliptic equation arising from the semilinear {Maxwell} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {839--842},
publisher = {Elsevier},
volume = {339},
number = {12},
year = {2004},
doi = {10.1016/j.crma.2004.07.029},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.07.029/}
}
TY - JOUR AU - Benci, Vieri AU - Fortunato, Donato TI - A strongly degenerate elliptic equation arising from the semilinear Maxwell equations JO - Comptes Rendus. Mathématique PY - 2004 SP - 839 EP - 842 VL - 339 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.07.029/ DO - 10.1016/j.crma.2004.07.029 LA - en ID - CRMATH_2004__339_12_839_0 ER -
%0 Journal Article %A Benci, Vieri %A Fortunato, Donato %T A strongly degenerate elliptic equation arising from the semilinear Maxwell equations %J Comptes Rendus. Mathématique %D 2004 %P 839-842 %V 339 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.07.029/ %R 10.1016/j.crma.2004.07.029 %G en %F CRMATH_2004__339_12_839_0
Benci, Vieri; Fortunato, Donato. A strongly degenerate elliptic equation arising from the semilinear Maxwell equations. Comptes Rendus. Mathématique, Tome 339 (2004) no. 12, pp. 839-842. doi : 10.1016/j.crma.2004.07.029. http://www.numdam.org/articles/10.1016/j.crma.2004.07.029/
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Cité par Sources :
* Conference given by the first author during the meeting, Journées à la mémoire de Guido Stampacchia, Paris, 31 March and 1 April 2003.
