Comptes Rendus
Partial Differential Equations
A strongly degenerate elliptic equation arising from the semilinear Maxwell equations
Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 839-842.

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.

Received:
Published online:
DOI: 10.1016/j.crma.2004.07.029
Vieri Benci 1; Donato Fortunato 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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Vieri Benci; Donato Fortunato. A strongly degenerate elliptic equation arising from the semilinear Maxwell equations. Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 839-842. doi : 10.1016/j.crma.2004.07.029. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.029/

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Cited by Sources:

* Conference given by the first author during the meeting, Journées à la mémoire de Guido Stampacchia, Paris, 31 March and 1 April 2003.

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