Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local recovery of a piecewise constant anisotropic conductivity in EIT
  on domains with exposed corners   We study the local recovery of an unknown piecewise constant anisotropic
conductivity in EIT (electric impedance tomography) on certain bounded
Lipschitz domains $\Omega$ in $\mathbb{R}^2$ with corners. The measurement is
conducted on a connected open subset of the boundary $\partial\Omega$ of
$\Omega$ containing corners and is given as a localized Neumann-to-Dirichlet
map. The above unknown conductivity is defined via a decomposition of $\Omega$
into polygonal cells. Specifically, we consider a parallelogram-based
decomposition and a trapezoid-based decomposition. We assume that the
decomposition is known, but the conductivity on each cell is unknown. We prove
the local recovery near a known piecewise constant anisotropic conductivity
$\gamma_0$. We do so by proving the injectivity of the Fr\'echet derivative
$F'(\gamma_0)$ of the forward map $F$, say, at $\gamma_0$. The proof presented,
here, involves defining different classes of decompositions for $\gamma_0$ and
a perturbation or contrast $H$ in a proper way so that we can find in the
interior of a cell for $\gamma_0$ exposed single or double corners of a cell of
$\mathrm{supp}H$ for the former decomposition and latter decomposition,
respectively. Then, by adapting the usual proof near such corners, we establish
the mentioned injectivity.

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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th