Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recent developments in applied pseudoanalytic function theory   We present recently obtained results in the theory of pseudoanalytic
functions and its applications to elliptic second-order equations. The operator
(divpgrad+q) with p and q being real valued functions is factorized with the
aid of Vekua type operators of a special form and as a consequence the elliptic
equation
  (divpgrad+q)u=0, (1) reduces to a homogeneous Vekua equation describing
generalized analytic (or pseudoanalytic) functions. As a tool for solving the
Vekua equation we use the theory of Taylor and Laurent series in formal powers
for pseudoanalytic functions developed by L. Bers. The series possess many
important properties of the usual analytic power series. Their applications
until recently were limited mainly because of the impossibility of their
explicit construction in a general situation. We obtain an algorithm which in a
really broad range of practical applications allows us to construct the formal
powers and hence the pseudoanalytic Taylor series in explicit form precisely
for the Vekua equation related to equation (1). In other words, in a bounded
domain this gives us a complete (in C-norm) system of exact solutions of (1).

22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int