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Uniqueness results for inverse Robin problems with bounded coefficient

Laurent Baratchart 1 Laurent Bourgeois 2 Juliette Leblond 1
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this paper we address the uniqueness issue in the classical Robin inverse problem on a Lipschitz domain $\Omega\subset\RR^n$, with $L^\infty$ Robin coefficient, $L^2$ Neumann data and isotropic conductivity of class $W^{1,r}(\Omega)$, $r>n$. We show that uniqueness of the Robin coefficient on a subpart of the boundary given Cauchy data on the complementary part, does hold in dimension $n=2$ but needs not hold in higher dimension. We also raise on open issue on harmonic gradients which is of interest in this context.
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https://hal.inria.fr/hal-01084428
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Submitted on : Thursday, February 11, 2016 - 6:43:33 PM
Last modification on : Friday, January 15, 2021 - 3:12:03 AM
Long-term archiving on: : Thursday, May 12, 2016 - 5:40:18 PM

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Laurent Baratchart, Laurent Bourgeois, Juliette Leblond. Uniqueness results for inverse Robin problems with bounded coefficient. Journal of Functional Analysis, Elsevier, 2016, ⟨10.1016/j.jfa.2016.01.011⟩. ⟨hal-01084428v2⟩

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