# Uniqueness results for inverse Robin problems with bounded coefficient

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1 APICS - Analysis and Problems of Inverse type in Control and Signal processing CRISAM - Inria Sophia Antipolis - Méditerranée 2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation Inria Saclay - Ile de France, ENSTA ParisTech 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.

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

Autor: Laurent Baratchart - Laurent Bourgeois - Juliette Leblond -

Fuente: https://hal.archives-ouvertes.fr/

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