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 $Ω\subset\RR^n$, 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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