The Calder\'on Problem For The Fractional Magnetic Operator

TL;DR

This paper introduces a fractional magnetic operator with potentials, formulates an inverse problem, and demonstrates the ability to recover electric potentials from partial boundary measurements using the Dirichlet-to-Neumann map.

Contribution

It is the first to address the inverse problem for the fractional magnetic operator and shows how to determine electric potentials from partial exterior data.

Findings

Electric potential can be uniquely recovered from partial boundary measurements.

The Runge approximation property is key to solving the inverse problem.

The approach extends classical inverse problems to fractional magnetic operators.

Abstract

We introduce the fractional magnetic operator involving a magnetic potential and an electric potential. We formulate an inverse problem for the fractional magnetic operator. We determine the electric potential from the exterior partial measurements of the associated Dirichlet-to-Neumann map by using Runge approximation property.