On the Calder\`on problem in periodic cylindrical domain with partial Dirichlet and Neumann data

TL;DR

This paper investigates the Calderón problem in an infinite cylindrical domain with partial boundary data, establishing a log-log stability estimate for determining the conductivity coefficient.

Contribution

It provides the first stability result for the Calderón problem in an infinite cylindrical setting with partial boundary measurements.

Findings

Proves log-log stability estimate for conductivity reconstruction.

Handles partial Dirichlet and Neumann boundary data.

Extends Calderón problem analysis to cylindrical geometries.

Abstract

We consider the Calder\`on problem in an infinite cylindrical domain, whose cross section is a bounded domain of the plane. We prove log-log stability in the determination of the isotropic periodic conductivity coefficient from partial Dirichlet data and partial Neumann boundary observations of the solution.