# Un problème inverse pour l’opérateur de Schrödinger avec condition au bord de type Neumann

## An inverse problem for the Schrödinger equation with Neumann boundary condition

Atef Saci
University of Batna 2
Algeria

Salah-Eddine Rebiai
University of Batna 2
Algeria

Publié le 12 janvier 2023   DOI : 10.21494/ISTE.OP.2023.0906

### Keywords

This article concerns the inverse problem of the recovery of unknown potential coefficient for the Schrödinger equation, in a bounded domain of ℝn with non-homogeneous Neumann boundary condition from a time-dependent Dirichlet boundary measurement. We prove uniqueness and Lipschitz stability for this inverse problem under certain convexity hypothesis on the geometry of the spatial domain and under weak regularity requirements on the data. The proof is based on a Carleman estimate in [12] for Schrödinger equations and its resulting implication, a continuous observability inequality.

This article concerns the inverse problem of the recovery of unknown potential coefficient for the Schrödinger equation, in a bounded domain of ℝn with non-homogeneous Neumann boundary condition from a time-dependent Dirichlet boundary measurement. We prove uniqueness and Lipschitz stability for this inverse problem under certain convexity hypothesis on the geometry of the spatial domain and under weak regularity requirements on the data. The proof is based on a Carleman estimate in [12] for Schrödinger equations and its resulting implication, a continuous observability inequality.