Asymptotic analysis of the scattering of a time-harmonic electromagnetic wave by a perfectly conducting metal coated with a thin dielectric shell

Our purpose is to investigate the effect of a thin dielectric coating on the scattering of a time-harmonic electromagnetic wave by a perfectly conducting metal. An asymptotic expansion of the solution of a model problem is performed relatively to the thickness of the dielectric shell. A suitable scaling as well as an adapted writing of the curl operator inside the thin shell make it possible to achieve an asymptotic expansion of the electromagnetic field at any order. Special stability estimates for Maxwell's equations relatively to the thickness of the dielectric shell then yield optimal error estimates outside the obstacle.