On the continuity dependence of elastic scattering amplitudes upon the shape of the scatterer

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Abstract
The transmission problem of linear elasticity in R2 is considered. The authors assume a system of quasi-Fredholm singular integral equations which describes the scattering process and they use an asymptotic analysis to derive relations for the far-field patterns. They establish a continuity dependence of the far-field patterns on the scatterer's shape. This result holds for a set of admissible functions which are considered as parametrization of the boundary of the inclusion. Continuity properties of this nature secure the stability of the inverse scattering problem.