Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toward the theory of semi-linear equations   In this paper we study the semilinear partial differential equations in the
plane the linear part of which is written in a divergence form. The main result
is given as a factorization theorem. This theorem states that every weak
solution of such an equation can be represented as a composition of a weak
solution of the corresponding isotropic equation in a canonical domain and a
quasiconformal mapping agreed with a matrix-valued measurable coefficient
appearing in the divergence part of the equation. The latter makes it possible,
in particular, to remove the regularity restrictions on the boundary in the
study of boundary value problems for such semilinear equations.

34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio