Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimates for solutions of the $\partial$-equation and application to
  the characterization of the zero varieties of the functions of the nevanlinna
  class for lineally convex domains of finite type   In the late ten years, the resolution of the equation $\bar\partial u=f$ with
sharp estimates has been intensively studied for convex domains of finite type
by many authors. In this paper, we consider the case of lineally convex
domains. As the method used to obtain global estimates for a support function
cannot be carried out in this case, we use a kernel that does not gives
directly a solution of the $\bar\partial$-equation but only a representation
formula which allows us to end the resolution of the equation using Kohn's
$L^2$ theory. As an application we give the characterization of the zero sets
of the functions of the Nevanlinna class for lineally convex domains of finite
type.

9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph