Skip to main content
Log in

An elementary proof for a compact imbedding result in generalized electromagnetic theory

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Adams, R.A.: Sobolev Spaces. New York: Academic Press 1975

    Google Scholar 

  2. Agmon, S.: Lectures on Elliptic Boundary Value Problems. Princeton: Van Nostrand 1965

    Google Scholar 

  3. Breinlinger, K.: Randwertaufgaben der Maxwellschen Gleichungen desR n für inhomogene Medien. Bonner Math. Schriften Nr. 37, Univ. of Bonn 1969

  4. Eidus, D.M.: Das Prinzip der Grenzabsorption. Mat. Sb. (N.S.)58 (100), 65–86 (1962) (Russian)

    Google Scholar 

  5. Fichera, G.: Teoria assiomatica delle forme armoniche. Rendiconti di Matematica, Roma20, 147–171 (1961)

    Google Scholar 

  6. Friedrichs, K.O.: Differential Forms on Riemannian Manifolds. Comm. Pure Appl. Math.8, 551–590 (1955)

    Google Scholar 

  7. Gaffney, M.: The harmonic operator for exterior differential forms. Proceedings of the National Science, U.S.A.,37, 48–50 (1951)

    Google Scholar 

  8. Hicks, N.J.: Notes on Differential Geometry, Princeton: Van Nostrand 1965

    Google Scholar 

  9. Kato, T.: Perturbation Theory for Linear Operators. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  10. König, H., Loch, H.: Eine abstrakte Theorie der Kegel- und Segmentbedingungen. Math. Meth. Appl. Sci.3 (1981)

  11. Morrey, C.B.: A Variational Method in the Theory of Harmonic Integrals II. Amer. Jour. Math.78, 137–170 (1956)

    Google Scholar 

  12. Morrey, C.B. Jr.: Multiple Integrals in the Calculus of Variations. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  13. Picard, R.: Ein Kompaktheitsresultat in der Theorie der verallgemeinerten Maxwell-Gleichung. SFB 72, Preprint Nr. 120, Univ. of Bonn 1977

  14. Picard, R.: Zur Existenz des Wellenoperators bei Anfangsrandwertproblemen vom Maxwell-Typ. Math. Z.156, 175–185 (1980)

    Google Scholar 

  15. Picard, R.: Randwertaufgaben der verallgemeinerten Potentialtheorie. Math. Meth. Appl. Sci.3, 218–228 (1981)

    Google Scholar 

  16. Picard, R.: On Boundary Value Problems of Electro- and Magnetostatics. Proc. Roy. Soc. Edin.92A, 165–174 (1982)

    Google Scholar 

  17. Picard, R.: Ein Hodge-Satz für Mannigfaltigkeiten mit nichtglattem Rand. Math. Meth. Appl. Sci.5, 153–161 (1983)

    Google Scholar 

  18. Picard, R.: Ein vereinheitlichter Zugang für eine Klasse linearer Wellenausbreitungs-Phänomene. Habilitation thesis, SFB 72, Preprint Nr. 489, Univ. of Bonn 1982

  19. Rinkens, H.D.: Zur Theorie der Maxwellschen Gleichungen in der Ebene. Bonner Math. Schriften, Nr. 38, Univ. of Bonn 1969

  20. Saranen, J.: On Electric and Magnetic Problems for Vector Fields in Anisotropic Nonhomogeneous Media. J. Math. Anal. Appl.91, 254–275 (1983)

    Google Scholar 

  21. Weber, C.: A local compactness theorem for Maxwell's equations. Math. Meth. Appl. Sci.2, 12–25 (1980)

    Google Scholar 

  22. Weck, N.: Eine Lösungstheorie für die Maxwellschen Gleichungen auf Riemannschen Mannigfaltigkeiten mit nicht-glattem Rand. Habilitation thesis, Univ. of Bonn 1972

  23. Weck, N.: Maxwell's Boundary Value Problem on Riemannian Manifolds with Nonsmooth Boundaries. J. Math. Anal. and Appl.46, 410–437 (1974)

    Google Scholar 

  24. Westenholz, C. von: Differential Forms in Mathematical Physics. Studies in Mathematics and its Applications, Amsterdam, North-Holland Publ. Comp. 1978

    Google Scholar 

  25. Weyl, H.: The Method of Orthogonal Projection in Potential Theory. Duke Math. J.7, 411–444 (1940)

    Google Scholar 

  26. Weyl, H.: Die natürlichen Randwertaufgaben im Außenraum für Strahlungsfelder beliebiger Dimension und beliebigen Ranges. Math. Z.56, 105–119 (1952)

    Google Scholar 

  27. Wilcox, C.H.: Scattering Theory for the D'Alembert Equation in Exterior Domains. Berlin-Heidelberg-New York: Springer 1975

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This paper is a publication of results obtained by the author in his habilitation thesis accepted by the Faculty of Mathematics and Science of the University of Bonn

Rights and permissions

Reprints and permissions

About this article

Cite this article

Picard, R. An elementary proof for a compact imbedding result in generalized electromagnetic theory. Math Z 187, 151–164 (1984). https://doi.org/10.1007/BF01161700

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01161700

Keywords

Navigation