Reconstruction of a potential from the impedance boundary map

Mikhail Isaev (1) , Roman Novikov (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We give formulas and equations for finding generalized scattering data for the Schrödinger equation in open bounded domain at fixed energy from the impedance boundary map (or Robin-to-Robin map). Combining these results with results of the inverse scattering theory we obtain efficient methods for reconstructing potential from the impedance boundary map.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Mikhail Isaev, Roman Novikov. Reconstruction of a potential from the impedance boundary map. Eurasian Journal of Mathematical and Computer Applications, 2013, 1 (1), pp.5-28. ⟨hal-00684169v2⟩