Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Wiener Test for the Removability of the Logarithmic Singularity for
  the Elliptic PDEs with Measurable Coefficients and Its Consequences   This paper introduces the notion of $log$-regularity (or $log$-irregularity)
of the boundary point $\zeta$ (possibly $\zeta=\infty$) of the arbitrary open
subset $\Omega$ of the Greenian deleted neigborhood of $\zeta$ in $R^2$
concerning second order uniformly elliptic equations with bounded and
measurable coefficients, according as whether the $log$-harmonic measure of
$\zeta$ is null (or positive). A necessary and sufficient condition for the
removability of the logarithmic singularity, that is to say for the existence
of a unique solution to the Dirichlet problem in $\Omega$ in a class $O(\log
|\cdot - \zeta|)$ is established in terms of the Wiener test for the
$log$-regularity of $\zeta$. From a topological point of view, the Wiener test
at $\zeta$ presents the minimal thinness criteria of sets near $\zeta$ in
minimal fine topology. Precisely, the open set $\Omega$ is a deleted
neigborhood of $\zeta$ in minimal fine topology if and only if $\zeta$ is
$log$-irregular. From the probabilistic point of view, the Wiener test presents
asymptotic law for the $log$-Brownian motion near $\zeta$ conditioned on the
logarithmic kernel with pole at $\zeta$.

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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
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys