TY  - Type of reference 
TI  - An inverse problem for the Schrödinger equation with Neumann boundary condition 
AU  - Atef Saci 
AU  - Salah-Eddine Rebiai 
AB  - 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. 
DO  - 10.21494/ISTE.OP.2023.0906 
JF  - Advances in Pure and Applied Mathematics 
KW  - Inverse problems,  Uniqueness,  Stability,  Schrodinger equations,  Carleman estimates, Inverse problems,  Uniqueness,  Stability,  Schrodinger equations,  Carleman estimates,  
L1  - https://openscience.fr/IMG/pdf/iste_apam23v14n1_4.pdf 
LA  - en 
PB  - ISTE OpenScience 
DA  - 2023/01/13 
SN  - 1869-6090 
TT  - Un problème inverse pour l’opérateur de Schrödinger avec condition au bord de type Neumann 
UR  - https://openscience.fr/An-inverse-problem-for-the-Schrodinger-equation-with-Neumann-boundary-condition 
IS  - Issue 1 (January 2023) 
VL  - 14 
ER  -