Domański, Włodzimierz Energy conserving boundary conditions for Maxwell’s equations in nonhomogeneous medium. (English) Zbl 0613.73107 Bull. Pol. Acad. Sci., Tech. Sci. 34, 215-223 (1986). The boundary conditions for the electromagnetic field can be discussed in terms of the energy balance. By physical reasons it is possible that there is no energy transport across the surface even for nonhomogeneous boundary conditions. In the paper presented here the problem of the electromagnetic field in a nonhomogeneous isotropic linear material with energy conserving boundary conditions is proved to be well-posed. For this purpose an inequality relating suitable weighted norms of the sought field and the given sources (or currents) in the spacial domain and at the surface is derived. The estimate is executed immediately for the simplified problem of the half space. Reviewer: G.Brunk MSC: 74F15 Electromagnetic effects in solid mechanics 78A25 Electromagnetic theory (general) 35L50 Initial-boundary value problems for first-order hyperbolic systems 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:electromagnetic field; energy balance; surface; nonhomogeneous isotropic linear material; energy conserving boundary conditions; well-posed; inequality PDFBibTeX XMLCite \textit{W. Domański}, Bull. Pol. Acad. Sci., Tech. Sci. 34, 215--223 (1986; Zbl 0613.73107)