Characterization of the Fréchet derivative of the elasto-acoustic field with respect to Lipschitz domains
Abstract
We establish the continuous Fréchet differentiability of the elasto-acoustic field with respect to Lipschitz continuous deformation of the shape of an elastic scatterer. We then characterize the derivative as a solution of a direct elasto-acoustic-type problem. Such a characterization has the potential to advance the state-of-the-art of the solution of inverse elasto-acoustic scattering problems.