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Zbl 0805.35157
Potthast, Roland
Fréchet differentiability of boundary integral operators in inverse acoustic scattering. (English)
[J] Inverse Probl. 10, No.2, 431-447 (1994). ISSN 0266-5611

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.

MSC 2000:: *35R30 Inverse problems for PDE
35P25 Scattering theory (PDE)
31B10 Integral representations of harmonic functions (higher-dimensional)

Keywords: Dirichlet boundary conditions; boundary integral equation of the second kind; scattered field

Cited in: Zbl 1020.35116

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