Inverse Problem for the Schrödinger Operator in an Unbounded Strip

Abstract

We consider the operator $H:=i{\partial }_t+\nabla \cdot (c\nabla )$ in an unbounded strip $\Omega$ in ${\mathbb{R}}^2$, where $c(x,y)\in {\mathcal{C}}^3(\bar{\Omega })$. 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 $c(x,y)$.