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Detecting perfectly insulated obstacles by shape optimization techniques of order two

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  • The paper extends investigations of identification problems by shape optimization methods for perfectly conducting inclusions to the case of perfectly insulating material. The Kohn and Vogelius criteria as well as a tracking type objective are considered for a variational formulation. In case of problems in dimension two, the necessary condition implies immediately a perfectly matching situation for both formulations. Similar to the perfectly conducting case, the compactness of the shape Hessian is shown and the ill-posedness of the identification problem follows. That is, the second order quadratic form is no longer coercive. We illustrate the general results by some explicit examples and we present some numerical results.
    Mathematics Subject Classification: Primary: 49Q10, 34A55; Secondary: 49Q12.


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