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

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.

Inverse problems Uniqueness Stability Schrodinger equations Carleman estimates

Inverse problems Uniqueness Stability Schrodinger equations Carleman estimates