Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstruction of isotropic conductivities from non smooth electric
  fields   In this paper we study the isotropic realizability of a given non smooth
gradient field $\nabla u$ defined in $\mathbb{R}^d$, namely when one can
reconstruct an isotropic conductivity $\sigma>0$ such that $\sigma\nabla u$ is
divergence free in $\mathbb{R}^d$. On the one hand, in the case where $\nabla
u$ is non-vanishing, uniformly continuous in $\mathbb{R}^d$ and $\triangle u$
is a bounded function in $\mathbb{R}^d$, we prove the isotropic realizability
of $\nabla u$ using the associated gradient flow combined with the DiPerna,
Lions approach for solving ordinary differential equations in suitable Sobolev
spaces. On the other hand, in the case where $\nabla u$ is piecewise regular,
we prove roughly speaking that the isotropic realizability holds if and only if
the normal derivatives of $u$ on each side of the gradient discontinuity
interfaces have the same sign. Some examples of conductivity reconstruction are
given.

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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an