On the Fréchet Derivative in Elastic Obstacle Scattering

In this paper, we investigate the existence and characterizations of the Fréchet derivatives of the solution to time-harmonic elastic scattering problems with respect to the boundary of the obstacle. Our analysis is based on a technique the factorization of the difference of the far-field pattern for two different scatterers introduced by Kress and Païvarinta to establish Fréchet differentiability in acoustic scattering. For the Dirichlet boundary condition an alternative proof of a differentiability result due to Charalambopoulos is provided and new results are proven for the Neumann and impedance exterior boundary value problems.