Static electromagnetic fields in monotone media

Rainer Picard

Banach Center Publications (1992)

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

Abstract

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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.

How to cite

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Picard, 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

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  1. [1] H. Brezis, Opérateurs Maximaux Monotones, North-Holland, Amsterdam 1973. 
  2. [2] K. O. Friedrichs, Differential forms on Riemannian manifolds, Comm. Pure Appl. Math. 8 (1955), 551-590. Zbl0066.07504
  3. [3] D. Graffi, Nonlinear Partial Differential Equations in Physical Problems, Pitman, Boston 1980. Zbl0453.35001
  4. [4] N. J. Hicks, Notes on Differential Geometry, Van Nostrand, Princeton 1965. 
  5. [5] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod-Gauthier-Villars, Paris 1969. Zbl0189.40603
  6. [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. [7] R. Picard, Randwertaufgaben der verallgemeinerten Potentialtheorie, Math. Methods Appl. Sci. 3 (1981), 218-228. Zbl0466.31016
  8. [8] R. Picard, On the boundary value problems of electro- and magnetostatics, Proc. Roy. Soc. Edinburgh 92A (1982), 165-174. Zbl0516.35023
  9. [9] R. Picard, An elementary proof for a compact imbedding result in generalized electromagnetic theory, Math. Z. 187 (1984), 151-164. Zbl0527.58038
  10. [10] R. Picard, The low frequency limit for time-harmonic acoustic waves, Math. Methods Appl. Sci. 8 (1986), 436-450. Zbl0609.35055
  11. [11] R. Picard, Some decomposition theorems and their application to non-linear potential theory and Hodge theory, ibid. 12 (1990), 35-52. 
  12. [12] C. Von Westenholz, Differential Forms In Mathematical Physics, Stud. In Math. Appl., North-Holland, Amsterdam 1978. Zbl0391.58001

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