Shape derivatives of boundary integral operators in electromagnetic scatterings. (arXiv:1002.1541v1 [math.NA])

Shape derivatives of boundary integral operators in electromagnetic scatterings. (arXiv:1002.1541v1 [math.NA]): "

We develop the shape derivative analysis of solutions to the problem of
scattering of time-harmonic electromagnetic waves by a bounded penetrable
obstacle. Since boundary integral equations are a classical tool to solve
electromagnetic scattering problems, we study the shape differentiability
properties of the standard electromagnetic boundary integral operators. We
prove that the electromagnetic boundary integral operators are infinitely
differentiable without loss of regularity and that the solutions of the
scattering problem are infinitely shape differentiable away from the boundary
of the obstacle, whereas their derivatives lose regularity on the boundary. We
also give a characterization of the first shape derivative as a solution of a
new electromagnetic scattering problem.

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