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Fréchet differentiability of boundary integral operators in inverse acoustic scattering. (English) Zbl 0805.35157
Summary: Using integral equation methods to solve the time-harmonic acoustic scattering problem with Dirichlet boundary conditions, 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 Fréchet differentiability of the boundary integral operators which occur. We then use this to prove the Fréchet differentiability of the scattered field with respect to the boundary. Finally we characterize the Fréchet derivative of the scattered field by a boundary value problem with Dirichlet conditions, in an analogous way to that used by Firsch.

35R30Inverse problems for PDE
35P25Scattering theory (PDE)
31B10Integral representations of harmonic functions (higher-dimensional)
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