Determining The Magnetic Potential In The Fractional Magnetic Calder\'on Problem

TL;DR

This paper develops methods to uniquely identify magnetic and electric potentials in fractional magnetic Calderón problems using exterior measurements and linearization techniques.

Contribution

It introduces new integral identity and linearization approaches to recover potentials in fractional magnetic Calderón problems, including nonlinear cases.

Findings

Unique determination of magnetic and electric potentials from exterior data

Extension to nonlinear fractional magnetic Calderón problems

Use of integral identities and linearization methods

Abstract

We determine both the magnetic potential and the electric potential from the exterior partial measurements of the Dirichlet-to-Neumann map in the fractional linear magnetic Calder\'on problem by using an integral identity. We also determine both the magnetic potential and the nonlinearity in the fractional semilinear magnetic Calder\'on problem by using a first order linearization.