Inverse boundary value problem for Schrödinger equation in cylindrical domain by partial boundary data

Abstract

Let $\Omega \subset {\mathbb{R}}^2$ be a bounded domain with $\partial \Omega \in C^{\infty }$ and $L$ be a positive number. For a three dimensional cylindrical domain $Q=\Omega \times (0,L)$, we obtain some uniqueness result of determining a complex-valued potential for the Schrödinger equation from partial Cauchy data when Dirichlet data vanish on a subboundary $(\partial \Omega \setminus \tilde{\Gamma })\times [0,L]$ and the corresponding Neumann data are observed on $\tilde{\Gamma }\times [0,L]$, where $\tilde{\Gamma }$ is an arbitrary fixed open set of $\partial \Omega .$

9 pages

References in corpus (3)

• Turbulence for the generalised Burgers equation
• Inverse problems with partial data for a magnetic Schrödinger operator in an infinite slab and on a bounded domain
• New global stability estimates for the Gel'fand-Calderon inverse problem

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