Article

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

04/2005; 12(1). DOI: 10.1088/1742-6596/12/1/003
Source: arXiv

ABSTRACT

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
$\partial\Omega_0$.

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• "More recently, the injectivity result for the non-abelian Radon transform was extended to any simply connected surface with strictly convex boundary and no conjugate points [30] and to higher dimensions and negative curvature [17]. There is a result due to G. Eskin [11] that implies Corollary 1.2 under the assumption that M is a domain in Euclidean space with obstacles. Our proof seems however simpler. "
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