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arXiv · 1412.3283

Uniqueness results for inverse Robin problems with bounded coefficient

Laurent Baratchart·Laurent Bourgeois·Juliette Leblond
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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 $W^{1,r}(\Omega)$, $r\textgreater{}n$. 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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Laurent Baratchart, Laurent Bourgeois, Juliette Leblond. 2014-12-10. Uniqueness results for inverse Robin problems with bounded coefficient. https://doi.org/10.1016/j.jfa.2016.01.011

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