Boundary Value Problems for Maxwell’s Equations

Abstract

This chapter is devoted to the mathematical investigation of a particular boundary value problem for Maxwell’s equation. We consider the time harmonic case, i.e. the equations (2.13a)–(2.13d), for the homogeneous and nonconducting case, i.e. when the permittivity and permeability, ε and μ, are constant and the conductivity σ = 0. We restrict ourselves to the boundary condition n × H = h on ∂Ω. For more complicated situations, in particular for the Leontovich (or impedance) and conductive boundary conditions we refer to [29], [5].