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The domain derivative for semilinear elliptic inverse obstacle problems

  • *Corresponding author: Frank Hettlich

    *Corresponding author: Frank Hettlich
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  • We consider the recovering of the shape of a cavity from the Cauchy datum on an accessible boundary in case of semilinear boundary value problems. Existence and a characterization of the domain derivative of solutions of semilinear elliptic equations are proven. Furthermore, the result is applied to solve an inverse obstacle problem with an iterative regularization scheme. By some numerical examples its performance in case of a Kerr type nonlinearity is illustrated.

    Mathematics Subject Classification: Primary: 35R30; Secondary: 35J61.


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  • Figure 1.  First and 10. iteration in case of noise free data, and the approximation errors versus iteration steps (reconstructions (red), initial guess (dotted, blue), exact object (dashed, black), residual error (blue), reconstruction error (dashed, red))

    Figure 2.  The worst and the best result from noisy data

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