On the Frechet derivative for obstacle scattering with an impedance boundary condition

Abstract

A technique introduced by Kress and Paivarinta to establish differentiability of the solution to obstacle scattering problems with respect to the boundary is extended to the case of the impedance boundary condition. For acoustic scattering an alternative proof of a differentiability result due to Hettlich is provided, and in electromagnetic scattering a new differentiability result is proven.