Maxwell’s equations with mixed impedance boundary conditions
Maxwell’s equations with mixed impedance boundary conditions
We study the time-harmonic Maxwell equations on bounded Lipschitz domains with an impedance boundary condition. The impedance coefficient can be matrix valued such that, in particular, a polarization dependent impedance is modeled. We derive a Fredholm alternative for this system. As a consequence, we obtain the existence of weak solutions for arbitrary sources when the frequency is not a resonance frequency. Our analysis covers the case of singular impedance coefficients.
19 pages
Impedance boundary condition, Polarization, Analysis of PDEs, FOS: Mathematics, 610, 35Q61, 78A25, 35A01, Maxwell’s equations, Analysis of PDEs (math.AP)
Impedance boundary condition, Polarization, Analysis of PDEs, FOS: Mathematics, 610, 35Q61, 78A25, 35A01, Maxwell’s equations, Analysis of PDEs (math.AP)
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