Milani, Albert; Negro, Angelo On the quasi-stationary Maxwell equations with monotone characteristics in a multiply connected domain. (English) Zbl 0507.35040 J. Math. Anal. Appl. 88, 216-230 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 Documents 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.) Keywords:quasi-stationary Maxwell equations; monotone characteristics; multiply connected domain; magnetic field distribution in transformer cores; magnetic core; existence; uniqueness; regularity PDFBibTeX XMLCite \textit{A. Milani} and \textit{A. Negro}, J. Math. Anal. Appl. 88, 216--230 (1982; Zbl 0507.35040) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.