Recovery of non compactly supported coefficients of elliptic equations on an infinite waveguide

TL;DR

This paper demonstrates the unique recovery of non-compactly supported electric potentials in unbounded waveguides from boundary measurements, advancing inverse problem techniques for unbounded domains.

Contribution

It proves the unique recovery of general electric potentials in unbounded cylindrical domains using partial boundary data, extending inverse problem results to non-compactly supported coefficients.

Findings

Unique recovery of electric potentials from partial boundary data.

Extension of inverse problem techniques to unbounded waveguides.

Application to recovery of coefficients in bounded and unbounded domains.

Abstract

We consider the unique recovery of a non compactly supported and non periodic perturbation of a Schr\"odinger operator in an unbounded cylindrical domain, also called waveguide, from boundary measurements. More precisely, we prove recovery of general class of electric potentials from the partial Dirichlet-to-Neumann map, where the Dirichlet data is supported on slightly more than half of the boundary and the Neumann data is taken on the other half of the boundary. We apply this result in different context including recovery of some general class of coefficients from measurements on a bounded subset and recovery of an electric potential, supported on an unbounded cylinder, of a Schr\"odinger operator in a slab.