We consider the inverse electromagnetic scatering problem of determining
the shape and surface impedance of a (possibly) partially coated perfect
conductor from a knowledge of the time harmonic electric far field
pattern at fixed frequency.Neither the connectivity nor the surface
impedance is known a priori.We detrmine the shape by the linear sampling
method and the norm of the surface impedance by a variational method.The
analysis is based on a study of mixed boundary value problems for
Maxwell's equations and approximation properties of electromagnetic
Herglotz pairs.
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