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Journal Articles Journal of Functional Analysis Year : 2016

Uniqueness results for inverse Robin problems with bounded coefficient

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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Dates and versions

hal-01084428 , version 1 (27-11-2014)
hal-01084428 , version 2 (11-02-2016)

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