Recovery of non compactly supported coefficients of an elliptic equation on an infinite waveguide

Yavar Kian (1, 2)

1 CPT - E8 Dynamique quantique et analyse spectrale
2 CPT - Centre de Physique Théorique - UMR 7332

We consider the unique recovery of a non compactly supported and non periodic perturbation of a Schrödinger operator in an unbounded cylindrical domain, also called waveguide, from boundary measurements. More precisely, we prove recovery of general class of electric potentials from the partial Dirichlet-to-Neumann map, where the Dirichlet data is supported on slightly more than half of the boundary and the Neumann data is taken on the other half of the boundary. We apply this result in different context including recovery of some general class of coefficients from measurements on a bounded subset and recovery of an electric potential, supported on an unbounded cylinder, of a Schrödinger operator in a slab.

Mots clés: Elliptic equation; scalar potential; unbounded domain; infinite cylindrical waveguide; slab; partial data; Carleman estimate

Domaines: Equations aux dérivées partielles [math.AP]

Yavar Kian. Recovery of non compactly supported coefficients of an elliptic equation on an infinite waveguide. Journal of the Institute of Mathematics of Jussieu, 2020, 19 (5), pp.1573 - 1600. ⟨10.1017/S1474748018000488⟩. ⟨hal-01583151⟩