Remark on Calder\'on's problem for the system of elliptic equations

TL;DR

This paper addresses Calderón's inverse problem for elliptic systems in two dimensions, proving that identical partial Dirichlet-to-Neumann maps imply unique determination of coefficients up to gauge transformations.

Contribution

It establishes the uniqueness of coefficients in elliptic systems from partial boundary measurements, extending Calderón's problem to systems in two dimensions.

Findings

Coefficients are uniquely determined up to gauge equivalence

Partial Dirichlet-to-Neumann map suffices for uniqueness

Results apply to systems of elliptic equations in 2D

Abstract

We consider the Calder\'on problem in the case of partial Dirichlet-to-Neumann map for the system of elliptic equations in a bounded two dimensional domain. The main result of the manuscript is as follows: If two systems of elliptic operators generate the same partial Dirichlet-to-Neumann map the coefficients can be uniquely determined up to the gauge equivalence.