On the Fréchet derivative in elastic obstacle scattering

Details On the Fréchet derivative in elastic obstacle scattering On the Fréchet derivative in elastic obstacle scattering

2011-03-07

arxiv.org/abs/1103.1229v1

Mathematics

Numerical Analysis

Scientific paper

In this paper, we investigate the existence and characterizations of the Fr\'echet 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 Pa\"ivarinta to establish Fr\'echet 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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