On the Fréchet Derivative for Obstacle Scattering with an Impedance Boundary Condition

A technique introduced by Kress and Päivärinta 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 He...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 65; no. 1; pp. 194 - 208
Main Authors Houssem Haddar, Kress, Rainer
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2004
Subjects
Acoustic impedance
Acoustics
Boundary conditions
Boundary value problems
Differential equations
Divergence theorem
Electric fields
Far fields
Helmholtz equations
Integral equations
Inverse problems
Mathematical integrals
Mathematics
Maxwell equations
Neighborhoods
Optimization and Control
Radiation
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Summary:A technique introduced by Kress and Päivärinta 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.
ISSN:0036-1399
1095-712X
DOI:10.1137/S0036139903435413