ANZIAM  J.  47 (2006), 397-411
On the low frequency asymptotics for the 2-D electromagnetic transmission problem

C. N. Anestopoulos
  National Technical University of Athens
  Department of Applied Mathematics and Physics
  GR-15780 Zografou Campus
E. E. Argyropoulos
  Technological Education Institute
  Department of Electrical Engineering
  GR-35100 Lamia

We examine the transmission problem in a two-dimensional domain, which consists of two different homogeneous media. We use boundary integral equation methods on the Maxwell equations governing the two media and we study the behaviour of the solution as the two different wave numbers tend to zero. We prove that as the boundary data of the general transmission problem converge uniformly to the boundary data of the corresponding electrostatic transmission problem, the general solution converges uniformly to the electrostatic one, provided we consider compact subsets of the domains.
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