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The determination of the surface conductivity of a partially coated dielectric. (English) Zbl 1083.78007
The authors consider the determination of the conducting surface of an object from a knowledge of the field scattered at a great distance. It is shown that this problem is not, in general, well-posed, unlike the complementary problem. They develop a variational method, using several abstract spaces, which gives a bound for the surface conductivity and give conditions for uniqueness to hold. It is pointed out that the result is valid for fully coated scatterers. Some numerical examples, using finite element methods are given but the detailed numerical analysis is given elsewhere. It is pointed out that the approximations deteriorate for large conductivities. The numerical results are illustrated by diagrams.
MSC:
78A46Inverse scattering problems
35R30Inverse problems for PDE
78A45Diffraction, scattering (optics)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation