Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conductivity imaging from one interior measurement in the presence of
  perfectly conducting and insulating inclusions   We consider the problem of recovering an isotropic conductivity outside some
perfectly conducting or insulating inclusions from the interior measurement of
the magnitude of one current density field $|J|$. We prove that the
conductivity outside the inclusions, and the shape and position of the
perfectly conducting and insulating inclusions are uniquely determined (except
in an exceptional case) by the magnitude of the current generated by imposing a
given boundary voltage. We have found an extension of the notion of
admissibility to the case of possible presence of perfectly conducting and
insulating inclusions. This also makes it possible to extend the results on
uniqueness of the minimizers of the least gradient problem
$F(u)=\int_{\Omega}a|\nabla u|$ with $u|_{\partial \Omega}=f$ to cases where
$u$ has flat regions (is constant on open sets).

15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an