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Inverse boundary value problem for Schrödinger equation in cylindrical domain by partial boundary data (1211.1419v1)
Published 6 Nov 2012 in math-ph, math.AP, and math.MP
Abstract: Let $\Omega\subset \Bbb R2$ 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 Schr\"odinger equation from partial Cauchy data when Dirichlet data vanish on a subboundary $(\partial\Omega\setminus\widetilde{\Gamma}) \times [0,L]$ and the corresponding Neumann data are observed on $\widetilde\Gamma \times [0,L]$, where $\widetilde\Gamma$ is an arbitrary fixed open set of $\partial\Omega.$