Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the fundamental solution and a variational formulation of a
  degenerate diffusion of Kolmogorov type   In this paper, we construct the fundamental solution to a degenerate
diffusion of Kolmogorov type and develop a time-discrete variational scheme for
its adjoint equation. The so-called mean squared derivative cost function plays
a crucial role occurring in both the fundamental solution and the variational
scheme. The latter is implemented by minimizing a free energy functional with
respect to the Kantorovich optimal transport cost functional associated with
the mean squared derivative cost. We establish the convergence of the scheme to
the solution of the adjoint equation generalizing previously known results for
the Fokker-Planck equation and the Kramers equation.

12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph