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

Journal of Physics Conference Series 04/2005; 12(1). DOI: 10.1088/1742-6596/12/1/003
Source: arXiv

ABSTRACT 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 .

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