Inverse Problem for the Schrödinger Operator in an Unbounded Strip

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

2006-12-19

arxiv.org/abs/math/0612539v2

Mathematics

Analysis of PDEs

Scientific paper

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 $c(x,y)$.

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