Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of Solutions for $\overline\partial$ Equation in Sobolev
  Spaces of Negative Index   Let $\Omega$ be a strictly pseudoconvex domain in $\mathbb{C}^n$ with
$C^{k+2}$ boundary, $k \geq 1$. We construct a $\overline\partial$ solution
operator (depending on $k$) that gains $\frac12$ derivative in the Sobolev
space $H^{s,p} (\Omega)$ for any $1<p<\infty$ and $s>\frac{1}{p} -k$. If the
domain is $C^{\infty}$, then there exists a $\overline\partial$ solution
operator that gains $\frac12$ derivative in $H^{s,p}(\Omega)$ for all $s \in
\mathbb{R}$. We obtain our solution operators through the method of homotopy
formula; a new feature is the construction of ``anti-derivative operators'' on
distributions defined on bounded Lipschitz domains.

20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph