Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sobolev regularity of the $\bar{\partial}$-equation on the Hartogs
  triangle   The regularity of the $\bar{\partial}$-problem on the domain
$\{|{z_1}|<|{z_2}|<1\}$ in $\mathbb{C}^2$ is studied using $L^2$ methods.
Estimates are obtained for the canonical solution in weighted $L^2$-Sobolev
spaces with a weight that is singular at the point $(0,0)$. The canonical
solution for $\dbar$ with weights is exact regular in the weighted Sobolev
spaces away from the singularity $(0,0)$. In particular, the singularity of the
Bergman projection for the Hartogs triangle is contained at the singular point
and it does not propagate.

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The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
6
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: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol