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research
Inverse problems for Schrodinger equations with Yang-Mills potentials in domains with obstacles and the Aharonov-Bohm effect
Authors
Belishev M
Belishev M
+9Â more
Eskin G
Eskin G
Eskin G
G Eskin
Isakov V
Katchalov A
Kurylev Y
Vainberg B
Varadarajan V S
Publication date
25 May 2005
Publisher
'IOP Publishing'
Doi
Cite
View
on
arXiv
Abstract
We study the inverse boundary value problems for the Schr\"{o}dinger equations with Yang-Mills potentials in a bounded domain
Ω
0
⊂
R
n
\Omega_0\subset\R^n
Ω
0
​
⊂
R
n
containing finite number of smooth obstacles
Ω
j
,
1
≤
j
≤
r
\Omega_j,1\leq j \leq r
Ω
j
​
,
1
≤
j
≤
r
. We prove that the Dirichlet-to-Neumann operator on
∂
Ω
0
\partial\Omega_0
∂
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
\partial\Omega_0
∂
Ω
0
​
.Comment: 15 page
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Last time updated on 03/12/2019