Determining the magnetic potential in the fractional magnetic Calderón problem

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 Calderón problem by using an integral identity. We also determine both the magnetic potential and the nonlinearity in the fractional semi-linear magnetic Calderón problem by using a first order linearization.

Keywords:

• Fractional partial differential equations
• inverse problems
• Runge approximation property

Acknowledgments

The author would like to thank Professor Gunther Uhlmann for suggesting the problem and for helpful discussions.

Additional information

Funding

The author is partly supported by National Science Foundation.