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


We study the inverse boundary value problems for the Schr\"{o}dinger
equations with Yang-Mills potentials in a bounded domain $\Omega_0\subset\R^n$
containing finite number of smooth obstacles $\Omega_j,1\leq j \leq r$. 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

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