Fréchet differentiability of the solution to the acoustic Neumann scattering problem with respect to the domain

ROLAND POTTHAST
1996 Journal of Inverse and Ill-Posed Problems  
Using integral equation methods to solve the time harmonic acoustic scattering problem with Neumann boundary condition it is possible to reduce the solution of the scattering problem to the solution of a boundary integral equation of the second kind. We show the Frechet differentiability of the boundary integral operators which occur. They are considered in dependence of the boundary as integral operators in the spaces of continuous functions. Then we use this to prove the Frechet
more » ... ity of the scattered fields. Finally we characterize the Frechet derivatives of the scattered fields by a suitable boundary value problem.
doi:10.1515/jiip.1996.4.1.67 fatcat:mxihabwjjbavxb46rkwwhc3vn4