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arXiv · 1012.4667

Global uniqueness and reconstruction for the multi-channel Gel'fand-Calderón inverse problem in two dimensions

Roman Novikov·Matteo Santacesaria
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Abstract

We study the multi-channel Gel'fand-Calderón inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation $-Δψ+ v(x) ψ= 0$, $x\in D$, where $v$ is a smooth matrix-valued potential defined on a bounded planar domain $D$. We give an exact global reconstruction method for finding $v$ from the associated Dirichlet-to-Neumann operator. This also yields a global uniqueness results: if two smooth matrix-valued potentials defined on a bounded planar domain have the same Dirichlet-to-Neumann operator then they coincide.

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Roman Novikov, Matteo Santacesaria. 2011-03-09. Global uniqueness and reconstruction for the multi-channel Gel'fand-Calderón inverse problem in two dimensions. https://doi.org/10.1016/j.bulsci.2011.04.007

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