Inverse Problem for the Schrödinger Operator in an Unbounded Strip

Laure Cardoulis (1) , Michel Cristofol (2) , Patricia Gaitan (2)

1 MIP - Mathématiques pour l'Industrie et la Physique
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We consider the operator $H:= i \partial_t + \nabla \cdot (c \nabla)$ in an unbounded strip $\Omega$ in $\mathbb{R}^2$, where $c(x,y) \in \mathcal{C}^3(\overline{\Omega})$. We prove adapted a global Carleman estimate and an energy estimate for this operator. Using these estimates, we give a stability result for the diffusion coefficient $c(x,y)$.

Mots clés: Inverse problem; Schrödinger operator; Unbounded strip; Carleman estimate

Domaines: Equations aux dérivées partielles [math.AP]

Laure Cardoulis, Michel Cristofol, Patricia Gaitan. Inverse Problem for the Schrödinger Operator in an Unbounded Strip. 2007. ⟨hal-00120940v3⟩