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 (2)

• 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