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

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

2010-12-21

arxiv.org/abs/1012.4667v3

Bulletin des Sciences Math\'ematiques 135, 5 (2011) 421-434

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.bulsci.2011.04.007

We study the multi-channel Gel'fand-Calder\'on inverse problem in two dimensions, i.e. the inverse boundary value problem for the equation $-\Delta \psi + v(x) \psi = 0$, $x\in D$, 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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