Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Dirichlet problem for a family of totally degenerate differential
  operators   In the framework of the Potential Theory we prove existence and uniqueness
for the Perron-Wiener-Brelot solution to the Dirichlet problem related to a
family of totally degenerate, in the sense of Bony, differential operators. We
also state and prove a Wiener-type criterium and an exterior cone condition for
boundary regularity.
  Our results apply to a wide family of strongly degenerate operators that
includes the following example~$\l = t^2\Delta_x + \langle x, \nabla_y \rangle
-\partial_t$, for~$(x,y,t) \in \R^N \times \R^{N} \times \R$.

29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol