Birman, M. Sh.; Solomyak, M. Z. The self-adjoint Maxwell operator in arbitrary domains. (English. Russian original) Zbl 0733.35099 Leningr. Math. J. 1, No. 1, 99-115 (1990); translation from Algebra Anal. 1, No. 1, 96-110 (1989). This paper deals with the presentation of \(L_ 2(\Omega)\)-theory for the Maxwell operator M in arbitrary regions \(\Omega\) filled with anisotropic medium under ideal conduction condition on the boundary \(\partial \Omega\). Note that the boundary \(\partial \Omega\) and matrix functions \(\epsilon\),\(\mu\) (dielectric and magnetic permeability) may be nonsmooth. In bounded domains the operator M describes electro-magnetic oscillations of a resonator and in unbounded domains - the scattering of electromagnetic waves by bounded or unbounded conductors. Reviewer: V.Makarov (Kiev) Cited in 17 Documents MSC: 35Q60 PDEs in connection with optics and electromagnetic theory 47F05 General theory of partial differential operators 78A25 Electromagnetic theory (general) 35J99 Elliptic equations and elliptic systems Keywords:nonsmooth coefficients and domains; Maxwell operator PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, Leningr. Math. J. 1, No. 1, 99--115 (1990; Zbl 0733.35099); translation from Algebra Anal. 1, No. 1, 96--110 (1989)