Stable recovery of non-compactly supported electromagnetic potentials in unbounded domain

TL;DR

This paper demonstrates the stable recovery of electromagnetic potentials in an unbounded cylindrical domain using boundary measurements, employing complex geometric optics solutions and Carleman estimates.

Contribution

It introduces a method for stable electromagnetic potential recovery in unbounded domains, extending previous techniques to non-compactly supported coefficients.

Findings

Stable recovery of magnetic and electric potentials from boundary data.

Results include partial boundary measurement stability.

Applicable to non-compactly supported coefficients in unbounded domains.

Abstract

We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and electric potential from boundary measurements. Assuming some knowledge of the unknown coefficients close to the boundary, we obtain also some results of stable recovery with measurements restricted to some portion of the boundary. Our approach combines construction of complex geometric optics solutions and Carleman estimates suitably designed for our stability results stated in an unbounded domain.