Diffraction at a curved grating. TM and TE cases,  homogenization.

Toufic  Abboud 
Centre de Mathematiques Appliquees - CNRS URA 756,
Ecole Polytechnique, 91128 Palaiseau Cedex, France.

Habib AMMARI 
Centre de Mathematiques Appliquees - CNRS URA 756,
Ecole Polytechnique, 91128 Palaiseau Cedex, France.



A hierachy of effective boundary conditions are derived for Helmholtz equation
with Dirichlet or Neumann boundary conditions. These generalized impedance
boundary conditions approximate the effect of thin dielectric layers with perfectly conducting inclusions covering
a body. Well-posedness of the problems with these new boundary conditions are proved
and optimal error estimates are given. 


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