The Calderón Problem For The Fractional Magnetic Operator

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.

arXiv comment14 pages

References in corpus (4)

• Ten equivalent definitions of the fractional Laplace operator
• Uniqueness and reconstruction for the fractional Calderón problem with a single measurement
• The Calderón problem for the fractional Schrödinger equation
• The fractional Calderón problem: low regularity and stability

Cited by in corpus (9)

• Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems
• The higher order fractional Calderón problem for linear local operators: uniqueness
• On an inverse problem for a fractional semilinear elliptic equation involving a magnetic potential
• Determining The Magnetic Potential In The Fractional Magnetic Calderón Problem
• A fractional parabolic inverse problem involving a time-dependent magnetic potential
• Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations
• An Inverse Problem for Non-linear Fractional Magnetic Schrodinger Equation
• The Calderón problem for nonlocal operators
• Integral geometry and unique continuation principles