Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Identifiability of Diffusion Coefficients for Source Terms of
  Non-Uniform Sign   The problem of recovering a diffusion coefficient $a$ in a second-order
elliptic partial differential equation from a corresponding solution $u$ for a
given right-hand side $f$ is considered, with particular focus on the case
where $f$ is allowed to take both positive and negative values. Identifiability
of $a$ from $u$ is shown under mild smoothness requirements on $a$, $f$, and on
the spatial domain $D$, assuming that either the gradient of $u$ is nonzero
almost everywhere, or that $f$ as a distribution does not vanish on any open
subset of $D$. Further results of this type under essentially minimal
regularity conditions are obtained for the case of $D$ being an interval,
including detailed information on the continuity properties of the mapping from
$u$ to $a$.

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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
18
The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph