Abstract
In the problem of the oscillations of a hollow resonator with ideally conducting walls, one describes the domain of definition of the corresponding self-adjoint Maxwell operator. One discusses the case when the boundary has inward edges.
Similar content being viewed by others
Literature cited
É. B. Bykhovskii and N. V. Smirnov, “On the orthogonal decomposition of the space of vector functions square-summable on a given domain and the operators of vector analysis,” Tr. Mat. Inst. Akad. Nauk SSSR,59, 5–36 (1960).
É. B. Bykhovskii, “Solution of the mixed problem for the system of Maxwell equations in the case of a perfectly conducting boundary,” Vestn. Leningr. Univ., No. 13, 50–66 (1957).
A. B. Alekseev and M. Sh. Birman, “A variational formulation of the problem of the oscillations of a resonator, filled with an anisotropic stratified medium,” Vestn. Leningr. Univ., Mat. Mekh. Astron., No. 7, Issue 2, 9–15 (1977).
O. A. Ladyzhenskaya, Mathematical Theory of Viscous Incompressible Flow, Gordan & Breach (1969).
H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung, in Handbuch der Physik, Band XXV/1, Springer, Berlin (1961), pp. 218–573.
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 3–9, 1985.
Rights and permissions
About this article
Cite this article
Birman, M.S. The maxwell operator in domains with edges. J Math Sci 37, 793–797 (1987). https://doi.org/10.1007/BF01387717
Issue Date:
DOI: https://doi.org/10.1007/BF01387717