Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-harmonic diffuse optical tomography: H\"older stability of the
  derivatives of the optical properties of a medium at the boundary   We study the inverse problem in Optical Tomography of determining the optical
properties of a medium $\Omega\subset\mathbb{R}^n$, with $n\geq 3$, under the
so-called diffusion approximation. We consider the time-harmonic case where
$\Omega$ is probed with an input field that is modulated with a fixed harmonic
frequency $\omega=\frac{k}{c}$, where $c$ is the speed of light and $k$ is the
wave number. Under suitable conditions that include a range of variability for
$k$, we prove a result of H\"older stability of the derivatives of the
absorption coefficient $\mu_a$ of any order at the boundary $\partial\Omega$ in
terms of the measurements, in the case when the scattering coefficient $\mu_s$
is assumed to be known. The stability estimates rely on the construction of
singular solutions of the underlying forward elliptic system, which extend
results obtained in J. Differential Equations 84 (2): 252-272 for the single
elliptic equation.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn