2 6 M ay 2 00 5 Inverse problems for Schrödinger equations with Yang - Mills potentials in domains with obstacles and the Aharonov - Bohm effect

We study the inverse boundary value problems for the Schrödinger equations with Yang-Mills potentials in a bounded domain Ω 0 ⊂ R n containing finite number of smooth obstacles Ω j , 1 ≤ j ≤ r. We prove that the Dirichlet-to-Neumann opeartor on ∂Ω 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 ∂Ω 0 .