Back to Search Start Over

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

Authors :
Novikov, Roman
Santacesaria, Matteo
Source :
Bulletin des Sciences Math\'ematiques 135, 5 (2011) 421-434
Publication Year :
2010

Abstract

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.

Details

Database :
arXiv
Journal :
Bulletin des Sciences Math\'ematiques 135, 5 (2011) 421-434
Publication Type :
Report
Accession number :
edsarx.1012.4667
Document Type :
Working Paper
Full Text :
https://doi.org/10.1016/j.bulsci.2011.04.007