The paper considers the static Maxwell system for a Lipschitz domain with perfectly conducting boundary. Electric and magnetic permeability ε and μ are allowed to be monotone and Lipschitz continuous functions of the electromagnetic field. The existence theory is developed in the framework of the theory of monotone operators.
@article{bwmeta1.element.bwnjournal-article-bcpv27z2p349bwm,
author = {Picard, Rainer},
title = {Static electromagnetic fields in monotone media},
journal = {Banach Center Publications},
volume = {27},
year = {1992},
pages = {349-360},
zbl = {0787.35112},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z2p349bwm}
}
Picard, Rainer. Static electromagnetic fields in monotone media. Banach Center Publications, Tome 27 (1992) pp. 349-360. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z2p349bwm/
[000] [1] H. Brezis, Opérateurs Maximaux Monotones, North-Holland, Amsterdam 1973.
[001] [2] K. O. Friedrichs, Differential forms on Riemannian manifolds, Comm. Pure Appl. Math. 8 (1955), 551-590. | Zbl 0066.07504
[002] [3] D. Graffi, Nonlinear Partial Differential Equations in Physical Problems, Pitman, Boston 1980. | Zbl 0453.35001
[003] [4] N. J. Hicks, Notes on Differential Geometry, Van Nostrand, Princeton 1965.
[004] [5] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod-Gauthier-Villars, Paris 1969. | Zbl 0189.40603
[005] [6] A. Milani and R. Picard, Decomposition theorems and their application to non-linear electro- and magneto-static boundary value problems, in: Partial Differential Equations and Calculus of Variations, Lecture Notes in Math. 1357, Springer, Berlin 1988, 317-340.
[006] [7] R. Picard, Randwertaufgaben der verallgemeinerten Potentialtheorie, Math. Methods Appl. Sci. 3 (1981), 218-228. | Zbl 0466.31016
[007] [8] R. Picard, On the boundary value problems of electro- and magnetostatics, Proc. Roy. Soc. Edinburgh 92A (1982), 165-174. | Zbl 0516.35023
[008] [9] R. Picard, An elementary proof for a compact imbedding result in generalized electromagnetic theory, Math. Z. 187 (1984), 151-164. | Zbl 0527.58038
[009] [10] R. Picard, The low frequency limit for time-harmonic acoustic waves, Math. Methods Appl. Sci. 8 (1986), 436-450. | Zbl 0609.35055
[010] [11] R. Picard, Some decomposition theorems and their application to non-linear potential theory and Hodge theory, ibid. 12 (1990), 35-52.
[011] [12] C. Von Westenholz, Differential Forms In Mathematical Physics, Stud. In Math. Appl., North-Holland, Amsterdam 1978. | Zbl 0391.58001