Inverse problems for Schrodinger equations with Yang-Mills potentials in domains with obstacles and the Aharonov-Bohm effect

Abstract

We study the inverse boundary value problems for the Schrödinger equations with Yang-Mills potentials in a bounded domain ${\Omega }_0\subset {\mathbb{R}}^n$ containing finite number of smooth obstacles ${\Omega }_j,1\le j\le r$. We prove that the Dirichlet-to-Neumann operator on $\partial {\Omega }_0$ determines the gauge equivalence class of the Yang-Mills potentials. We also prove that the metric tensor can be recovered up to a diffeomorphism that is identity on $\partial {\Omega }_0$.

15 pages

Cited by in corpus (6)

• A new approach to hyperbolic inverse problems
• Inverse problems for general second order hyperbolic equations with time-dependent coefficients
• A new approach to hyperbolic inverse problems II (Global step)
• A Simple Proof of Magnetic and Electric Aharonov-Bohm Effects
• Aharonov-Bohm effect revisited
• Mathematical Modeling for Tomography in Domains with Reflecting Obstacles