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

preprint2012arXivOpen access

Abstract

Let Ω⊂R2Ω\subset \Bbb R^2 be a bounded domain with ∂Ω∈C∞\partialΩ\in C^\infty and LL be a positive number. For a three dimensional cylindrical domain Q=Ω×(0,L)Q=Ω\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 (∂Ω∖Γ~)×[0,L](\partialΩ\setminus\widetildeΓ) \times [0,L] and the corresponding Neumann data are observed on Γ~×[0,L]\widetildeΓ\times [0,L], where Γ~\widetildeΓ is an arbitrary fixed open set of ∂Ω.\partialΩ.

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