Comptes Rendus
no. 12
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

Vieri Benci1 ; Donato Fortunato2
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, Volume 339 (2004) no. 12, pp. 839-842.

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.

Reçu le :
Publié le :
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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  • Alireza Khatib; Liliane A. Maia A note on a positive solution of a null mass nonlinear field equation in exterior domains, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 150 (2020) no. 2, p. 841 | DOI:10.1017/prm.2018.125
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Cité par 3 documents. Sources : Crossref

* 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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