Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Dirichlet problem and prime ends   It is developed the theory of the boundary behavior of homeomorphic solutions
of the Beltrami equations ${\bar{\partial}}f=\mu\,{\partial}f$ of the Sobolev
class $W^{1,1}_{\rm loc}$ with respect to prime ends of domains. On this basis,
under certain conditions on the complex coefficient ${\mu}$, it is proved the
existence of regular solutions of its Dirichlet problem in arbitrary simply
connected domains and pseudoregular as well as multivalent solutions in
arbitrary finitely connected domains with continuous boundary data in terms of
prime ends.

16
The categories of this paper are: stat
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn