On the use of T-coercivity to study the interior transmission eigenvalue problem |
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Authors: | Anne-Sophie Bonnet-Ben Dhia Lucas Chesnel Houssem Haddar |
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Institution: | 1. POEMS, UMR 7231 CNRS-INRIA-ENSTA, 32, boulevard Victor, 75739 Paris cedex 15, France;2. INRIA Saclay Ile de France / École polytechnique, route de Saclay, 91128 Palaiseau cedex, France |
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Abstract: | In this Note, we investigate the so-called interior transmission problem using the T-coercivity approach. In particular, we prove that this problem, which appears when one is interested in the reconstruction of the support of an inclusion embedded in a homogeneous medium, is of Fredholm type and that so-called transmission eigenvalues form at most a discrete set. Our approach treats cases where the difference between the inclusion index and the background index can change sign, which are not covered by other techniques that can be found in the literature. We also provide Faber–Krahn type inequalities associated with this general case. |
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