Uniqueness results for 2D 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

We address in this work the uniqueness issue in the classical Robin inverse problem with the Laplace equation on a Dini-smooth planar domain, with uniformly bounded Robin coefficient and L2 Neumann data. We prove uniqueness of the Robin coefficient on a subpart of the boundary, given Cauchy data on the complementary part.

Mots clés: complex analysis; unique continuation; Robin inverse problem; Hardy space H2; holomorphic functions; Dini-smooth domain

Domaines: Mathématiques [math]

Laurent Baratchart, Laurent Bourgeois, Juliette Leblond. Uniqueness results for 2D inverse Robin problems with bounded coefficient. [Research Report] RR-8665, INRIA Sophia Antipolis; INRIA Saclay; INRIA. 2015. ⟨hal-01104629⟩