Abstract: We consider the direct and inverse scattering problems for partially coated obstacles. To this end, we first use the method of integral equations of the first kind to solve
a scattering problem for the Helmholtz equation where the scattered field satisfies mixed
Dirichlet-impedance boundary conditions on the Lipschitz boundary of the scatterer D. We
then use the linear sampling method to solve the inverse scattering problem of determining
D from a knowledge of the far field pattern of the scattered field. Numerical examples are
given showing the performance of the linear sampling method in this case.
