Geodesic
Partial Differential Equations
A strongly degenerate elliptic equation arising from the semilinear Maxwell equations
[Une équation elliptique fortement dégénérée provenant des équations de Maxwell semilinéaires.]

Présenté par : Haïm Brezis

Benci, Vieri1 ; Fortunato, Donato2
1 Dipartimento di Matematica Applicata ‘U. Dini’, Università degli Studi di Pisa Università di Pisa, via Bonanno, 25/b, 56126 Pisa, Italy
2 Dipartimento di Matematica, Università di Bari, Via Orabona, 4, 70125 Bari, Italy
Comptes Rendus. Mathématique, Tome 339 (2004) no. 12, pp. 839-842.

Voir la notice de l'article provenant de la source Numdam

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.

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.

Reçu le :
Publié le :
DOI : 10.1016/j.crma.2004.07.029

Benci, Vieri 1 ; Fortunato, Donato 2

1 Dipartimento di Matematica Applicata ‘U. Dini’, Università degli Studi di Pisa Università di Pisa, via Bonanno, 25/b, 56126 Pisa, Italy
2 Dipartimento di Matematica, Università di Bari, Via Orabona, 4, 70125 Bari, Italy 
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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://geodesic.mathdoc.fr/articles/10.1016/j.crma.2004.07.029/

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[3] Benci, V.; Rabinowitz, P.H. Critical points theorems for indefinite functionals, Invent. Math., Volume 52 (1979), pp. 241-273

[4] Born, M.; Infeld, L. Foundations of the new field theory, Proc. Roy. Soc. London A, Volume 144 (1934), pp. 425-451

[5] Castro, A.; Lazer, A.C. Applications of a min-max principle, Rev. Colombiana Mat., Volume 10 (1976), pp. 141-149

[6] Esteban, M.; Sere, E. Stationary states of the nonlinear Dirac equation: a variational approach, Commun. Math. Phys., Volume 171 (1995), pp. 323-350

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.