A problem of magnetostatics related to thin plates
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 32 (1998) no. 7, p. 859-876
@article{M2AN_1998__32_7_859_0,
     author = {Descloux, Jean and Flueck, Michel and Romerio, Michel V.},
     title = {A problem of magnetostatics related to thin plates},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {32},
     number = {7},
     year = {1998},
     pages = {859-876},
     zbl = {0914.65127},
     mrnumber = {1654515},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1998__32_7_859_0}
}
Descloux, Jean; Flueck, Michel; Romerio, Michel V. A problem of magnetostatics related to thin plates. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 32 (1998) no. 7, pp. 859-876. http://www.numdam.org/item/M2AN_1998__32_7_859_0/

[1] A. G. Armstrong, A. M. Collie, C. J. Diserens, N. J. Newman, M. Simkin and C. W. Trowbridge, New developments in the magnet design program GFUN. Rutherford Laboratory Report RL-5060.

[2] Sh. Axler, P. Bourdon and W. Ramey, Harmonic function theory. Graduate Texts in Mathematics, 137, Springer-Verlag, New York, 1992. | MR 1184139 | Zbl 0765.31001

[3] A. Bossavit, On the condition "H normal to the wall" in magnetic field problems. Écoles CEA-EDF-INRIA: Magnétostatique, pages 9-28, INRIA 1987. | Zbl 0616.65125

[4] P. G. Ciarlet, Plates and junctions in elastic multi-structures. An asymptotic analysis. Masson-Springer Verlag, Paris, 1990. | MR 1071376 | Zbl 0706.73046

[5] M. Friedman, Finite element formulation of the general magnetostatic problem in the space of solenoidal vector functions. Math. of Comp., 43: pp. 415-431, 1984. | MR 758191 | Zbl 0561.65093

[6] J. K. Hale and G. Raugel, Partial differential equations on thin domains. In Differential equations and mathematical physics. Mathematics in science and engineering, 186, edited by Ch. Bennewitz, Academic Press, Boston, 1992. | MR 1126691 | Zbl 0785.35050

[7] H. Le Dret, Problèmes variationnels dans les multi-domaines. Modélisation des jonctions et applications. Masson, Paris, 1991. | MR 1130395 | Zbl 0744.73027

[8] J.-L. Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal. Lecture Notes in Mathematics, 323, Springer-Verlag, Berlin, 1973. | MR 600331 | Zbl 0268.49001

[9] J. Pasciak, A new scalar potential formulation of the magnetostatic field problem. Math. of Comp., 43: pp. 433-445, 1984. | MR 758192 | Zbl 0552.65082

[10] G. Raugel and G. Sell, Équations de Navier-Stokes dans des domaines minces en dimension trois : régularité globale. C. R. Acad. Sci. Paris, Série I, Math. 309 : pp. 299-303, 1989. | MR 1054239 | Zbl 0715.35063

[11] F. Rogier, Mathematical and numerical stùdy of a magnetostatic problem around a thin shield. SIAM J. Numer. Anal., 30: pp. 454-477, 1993. | MR 1211400 | Zbl 0773.65086

[12] R. Temam and M. Ziane, Navier-Stokes equations in three-dimensional thin domains with various boundary conditions. Advances in Differential Equations, 1: pp. 499-546, 1996. | MR 1401403 | Zbl 0864.35083

[13] M. Vainberg, Variational method and method of monotone operators in the theory of nonlinear operators. John Wiley and Sons, New York, Toronto, 1973.

[14] R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Masson, Paris, 1985. | Zbl 0642.35001