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## Inverse Problem for the Schrödinger Operator in an Unbounded Strip

Laure Cardoulis
• Function : Author
Michel Cristofol
Patricia Gaitan
• Function : Author
• PersonId : 832732

#### Abstract

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 $c(x,y)$.

#### Domains

Mathematics [math] Analysis of PDEs [math.AP]

### Dates and versions

hal-00120940 , version 1 (18-12-2006)
hal-00120940 , version 2 (13-09-2007)
hal-00120940 , version 3 (13-09-2007)

### Identifiers

• HAL Id : hal-00120940 , version 3
• ARXIV :

### Cite

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

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