# Static electromagnetic fields in monotone media

Banach Center Publications (1992)

- Volume: 27, Issue: 2, page 349-360
- ISSN: 0137-6934

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topPicard, Rainer. "Static electromagnetic fields in monotone media." Banach Center Publications 27.2 (1992): 349-360. <http://eudml.org/doc/262835>.

@article{Picard1992,

abstract = {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.},

author = {Picard, Rainer},

journal = {Banach Center Publications},

keywords = {uniqueness; continuous dependence; static Maxwell system; Lipschitz domain; perfectly conducting boundary; existence; monotone operators},

language = {eng},

number = {2},

pages = {349-360},

title = {Static electromagnetic fields in monotone media},

url = {http://eudml.org/doc/262835},

volume = {27},

year = {1992},

}

TY - JOUR

AU - Picard, Rainer

TI - Static electromagnetic fields in monotone media

JO - Banach Center Publications

PY - 1992

VL - 27

IS - 2

SP - 349

EP - 360

AB - 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.

LA - eng

KW - uniqueness; continuous dependence; static Maxwell system; Lipschitz domain; perfectly conducting boundary; existence; monotone operators

UR - http://eudml.org/doc/262835

ER -

## References

top- [1] H. Brezis, Opérateurs Maximaux Monotones, North-Holland, Amsterdam 1973.
- [2] K. O. Friedrichs, Differential forms on Riemannian manifolds, Comm. Pure Appl. Math. 8 (1955), 551-590. Zbl0066.07504
- [3] D. Graffi, Nonlinear Partial Differential Equations in Physical Problems, Pitman, Boston 1980. Zbl0453.35001
- [4] N. J. Hicks, Notes on Differential Geometry, Van Nostrand, Princeton 1965.
- [5] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod-Gauthier-Villars, Paris 1969. Zbl0189.40603
- [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.
- [7] R. Picard, Randwertaufgaben der verallgemeinerten Potentialtheorie, Math. Methods Appl. Sci. 3 (1981), 218-228. Zbl0466.31016
- [8] R. Picard, On the boundary value problems of electro- and magnetostatics, Proc. Roy. Soc. Edinburgh 92A (1982), 165-174. Zbl0516.35023
- [9] R. Picard, An elementary proof for a compact imbedding result in generalized electromagnetic theory, Math. Z. 187 (1984), 151-164. Zbl0527.58038
- [10] R. Picard, The low frequency limit for time-harmonic acoustic waves, Math. Methods Appl. Sci. 8 (1986), 436-450. Zbl0609.35055
- [11] R. Picard, Some decomposition theorems and their application to non-linear potential theory and Hodge theory, ibid. 12 (1990), 35-52.
- [12] C. Von Westenholz, Differential Forms In Mathematical Physics, Stud. In Math. Appl., North-Holland, Amsterdam 1978. Zbl0391.58001

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