[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 :
Vieri Benci 1 ; Donato Fortunato 2
@article{CRMATH_2004__339_12_839_0, author = {Vieri Benci and Donato Fortunato}, 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}, }
TY - JOUR AU - Vieri Benci AU - Donato Fortunato 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 DO - 10.1016/j.crma.2004.07.029 LA - en ID - CRMATH_2004__339_12_839_0 ER -
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/
[1] Towards a unified field theory for classical electrodynamics, Arch. Rational Mech. Anal., Volume 173 (2004), pp. 379-414
[2] On the existence of infinitely many geodesics on space–time manifolds, Adv. Math., Volume 105 (1994), pp. 1-25
[3] Critical points theorems for indefinite functionals, Invent. Math., Volume 52 (1979), pp. 241-273
[4] Foundations of the new field theory, Proc. Roy. Soc. London A, Volume 144 (1934), pp. 425-451
[5] Applications of a min-max principle, Rev. Colombiana Mat., Volume 10 (1976), pp. 141-149
[6] 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.
Commentaires - Politique