Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toward the theory of Dirichlet problem for the degenerate Beltrami
  equations   In this article, first we give a general lemma on the existence of regular
homeomorphic solutions $f$ with the hydrodynamic normalization $f(z)=z+o(1)$ as
$z\to\infty$ to the degenerate Beltrami equations
$\overline{\partial}f=\mu\,\partial f$ in $\mathbb C$ whose complex
coefficients $\mu$ have compact supports. On this basis, we establish criteria
for existence and representation of regular discrete open solutions for the
Dirichlet problem with continuous data to degenerate Beltrami equations in
arbitrary simply connected bounded domains $D$ in $\mathbb C$.
  Moreover, we obtain similar criteria for the existence of multi-valued
solutions $f$ in the spirit of the theory of multi-valued analytic functions in
arbitrary bounded domains $D$ in $\mathbb C$ with no boundary component
degenerated to a single point. Note that the latter request is necessary and
that the real parts $u$ of such solutions $f$ are the so-called $A-$harmonic
functions, i.e., single-valued continuous weak solutions of elliptice quations
${\rm div}\, (A\cdot\nabla u)=0$ with matrix-valued coefficients $A$ associated
with $\mu$. Thus, the results can be applied to potential theory in anisotropic
and inhomogeneous media.

32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga