Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An inverse problem for the magnetic Schr\"odinger equation in infinite
  cylindrical domains   We study the inverse problem of determining the magnetic field and the
electric potential entering the Schr\"odinger equation in an infinite 3D
cylindrical domain, by Dirichlet-to-Neumann map. The cylindrical domain we
consider is a closed waveguide in the sense that the cross section is a bounded
domain of the plane. We prove that the knowledge of the Dirichlet-to-Neumann
map determines uniquely, and even H\"older-stably, the magnetic field induced
by the magnetic potential and the electric potential. Moreover, if the maximal
strength of both the magnetic field and the electric potential, is attained in
a fixed bounded subset of the domain, we extend the above results by taking
finitely extended boundary observations of the solution, only.

12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat