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

Abstract

We study the multi-channel Gel'fand-Calderón 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.

References in corpus (3)

• A global stability estimate for the Gel'fand-Calderon inverse problem in two dimensions
• New global stability estimates for the Gel'fand-Calderon inverse problem
• Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

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• Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials
• Monochromatic reconstruction algorithms for two-dimensional multi-channel inverse problems
• Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations
• Global stability for the multi-channel Gel'fand-Calderón inverse problem in two dimensions
• Energy and regularity dependent stability estimates for near-field inverse scattering in multidimensions