Global uniqueness and reconstruction for the multi-channel Gel'fand-Calderón inverse problem in two dimensions (Q554225)

Let \(D\) be a bounded domain in \(\mathbb R^2\). The paper under review is concerned with the inverse boundary problem for the linear elliptic equation \(\Delta\psi =v(x)\psi\) in \(D\), where \(v\) is a smooth matrix-valued potential. The main result in this paper establishes an exact global reconstruction method for finding \(v\) from the associated boundary operator. A global uniqueness result is also provided. The results in the present paper are motivated by phenomena arising in quantum mechanics, acoustics or electrodynamics.