@ARTICLE{10.21494/ISTE.OP.2023.0906, 

TITLE={An inverse problem for the Schrödinger equation with Neumann boundary condition}, 
  
AUTHOR={Atef Saci, Salah-Eddine Rebiai, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={14}, 

NUMBER={Issue 1 (January 2023)}, 
	
YEAR={2023}, 

URL={https://openscience.fr/An-inverse-problem-for-the-Schrodinger-equation-with-Neumann-boundary-condition}, 
	
DOI={10.21494/ISTE.OP.2023.0906}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={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.}}