Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction by similarity method of the fundamental solution of the
  Dirichlet problem for Keldysh type equation in the half-space   For elliptic in the half-space and parabolic degenerating on the boundary
equation of Keldysh type we construct by similarity method the self-similar
solution, which is the approximation to the identity in the class of integrable
functions. This solution is the fundamental solution of the Dirichlet problem,
i.e. the solution of the Dirichlet problem with the Dirac delta-function in the
boundary condition. Solution of the Dirichlet problem with an arbitrary
function in the boundary condition can be written as the convolution of the
function with the fundamental solution of the Dirichlet problem, if a
convolution exists. For a bounded and piecewise continuous boundary function
convolution exists and is written in the form of an integral, which gives the
classical solution of the Dirichlet problem, and is a generalization of the
Poisson integral for the Laplace equation. If the boundary function is a
generalized function, the convolution is a generalized solution of the
Dirichlet problem.

30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga