On the Fréchet Derivative in Elastic Obstacle Scattering

In this paper, we investigate the existence and characterizations of the Frechet derivative of solutions 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 Paivarinta [SIAM J. Appl. Math., 59 (1999), pp. 1413--1426] to establish Frechet 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.

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