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 $Ω_0\subset\R^n$ containing finite number of smooth obstacles $Ω_j,1\leq j \leq r$. We prove that the Dirichlet-to-Neumann operator on $\partialΩ_0$ 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 $\partialΩ_0$.