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On the quasi-stationary Maxwell equations with monotone characteristics in a multiply connected domain. (English) Zbl 0507.35040


MSC:

35K50 Systems of parabolic equations, boundary value problems (MSC2000)
78A30 Electro- and magnetostatics
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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[1] Brézis, H., Operateurs maximaux monotones, (Notas de Matematica No. 5 (1973), North-Holland: North-Holland Amsterdam) · Zbl 0252.47055
[2] Duff, G. F., Differential forms in manifolds with boundary, Ann. of Math., 56, No. 1, 115-127 (1952) · Zbl 0049.18804
[3] Duff, G. F., On the potential theory of coclosed harmonic forms, Canad. J. Math., 7, 126-137 (1955) · Zbl 0064.09202
[4] Duff, G. F., Various classes of harmonic forms, (Fox, R. H.; etal., Algebric Geometry and Topology (1957), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J) · Zbl 0083.32501
[5] Duvaut, G.; Lions, J. L., Les inéquations en mécanique et en physique (1969), Dunod/Gauthier-Villars: Dunod/Gauthier-Villars Paris · Zbl 0298.73001
[6] Foias, C.; Temam, R., Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes succesifs de bifurcation, Ann. Univ. Pisa, 4, 29-36 (1978) · Zbl 0384.35047
[7] Friedrichs, K. O., Differential forms on Riemannian manifolds, Comm. Pure Appl. Math., 8, 551-590 (1955) · Zbl 0066.07504
[8] Hodge, W. V.D, The Theory and Applications of Harmonic Integrals (1952), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0048.15702
[9] Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires (1969), Dunod/Gauthier-Villars: Dunod/Gauthier-Villars Paris · Zbl 0189.40603
[10] Negro, A., A time periodic boundary value problem for non linear quasi-stationary Maxwell equations, Boll. Un. Mat. Ital. B(5), 17, 604-613 (1980) · Zbl 0441.35017
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