Uniqueness results for inverse Robin problems with bounded coefficient

Laurent Baratchart (1) , Laurent Bourgeois (2) , Juliette Leblond (1)

1 APICS - Analysis and Problems of Inverse type in Control and Signal processing
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

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.

Mots clés: holomorphic Hardy–Smirnov classes; harmonic analysis; complex analysis; Robin inverse problem; unique continuation; Sobolev spaces; elliptic regularity

Domaines: Equations aux dérivées partielles [math.AP]

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⟩