Department of Mathematics

Speaker: Alexandru Tamasan
Title: Conductivity Imaging from Minimal Interior Data
Affiliation: University of Central Florida
Date: Thursday, November 10, 2011
Place and Time: Room 200, Love Building, 3:35-4:30 pm

Abstract. This talk considers the inverse problem of conductivity imaging from knowledge of the magnitude of one current density field inside. This problem belongs to the recent trend in Inverse Problems of imaging from coupled physics. Mathematically, the problem leads to the 1-Laplacian (a degenerate elliptic) equation in a metric space conformal with Euclidean, with a factor determined by the interior data. The starting observation is that equipotential surfaces are minimal surfaces in this space. Unique identification can be shown via the uniqueness in a degenerate, non-smooth optimization problem. In some cases, the viscosity solution of the PDE which are minimizers in the functional approach can be understood as limiting cases in which some perfectly conducting/insulating regions are embedded inside. The talk is based on various results obtained in collaborative work with A. Nachman, A. Moradifam, Z. Nashed, or A. Timonov.