Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the $L^2$-Dolbeault cohomology of annuli   For certain annuli in $\mathbb{C}^n$, $n\geq 2$, with non-smooth holes, we
show that the $\bar{\partial}$-operator from $L^2$ functions to $L^2$
$(0,1)$-forms has closed range. The holes admitted include products of
pseudoconvex domains and certain intersections of smoothly bounded pseudoconvex
domains. As a consequence, we obtain estimates in the Sobolev space $W^1$ for
the $\bar{\partial}$-equation on the non-smooth domains which are the holes of
these annuli.

8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph