On the exterior boundary value problem of perfect reflection for stationary electromagnetic wave fields

Abstract

Abstract : The boundary value problem is reduced to a system of Fredholm integral equations which is solvable for all positive frequencies. The numerical computation of the solutions which previously contained considerable difficulties when the electrical conductivit was zero or small, can now be placed on a rigorous foundation. Important dependence properties can be derived which could not be established within the previous framework.As a consequence, the radiation conditions which were previously employed to characterize the physicall relevant solutions can be replaced by the principle of limiting absorption which seems to be much more satisfactory from a physical point of view. The behaviour of the stationary electromagnetic field is discussed. Final results in this direction are only obtained under the additional assumption that all reflecting bodies are simply connected. It is proven that the electric field E tends analyticall to a corresponding electrostatic field. This leads to a mathematical foundation of some assumptions often used in the theory of low frequency approximations. (Author)