Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Harnack inequality and H\"older continuity for weak solutions to
  parabolic operators involving H\"ormander vector fields   This paper deals with two separate but related results. First we consider
weak solutions to a parabolic operator with H\"ormander vector fields. Adapting
the iteration scheme of J\"urgen Moser for elliptic and parabolic equations in
$\mathbb{R}^n$ we show a parabolic Harnack inequality. Then, after proving the
Harnack inequality for weak solutions to equations of the form $u_t = \sum X_i
(a_{ij} X_j u)$ we use this to show H\"older continuity. We assume the
coefficients are bounded and elliptic. The iteration scheme is a tool that may
be adapted to many settings and we extend this to nonlinear parabolic equations
of the form $u_t = -X_i^* A_j(X_j u)$. With this we show both a Harnack
inequality and H\"older continuity of weak solutions.

5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
1
The categories of this paper are: cs