Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Strong unique continuation property of a degenerate elliptic
  operator with Hardy type potential   In this paper we prove strong unique continuation for the following
degenerate elliptic equation \begin{equation}\label{e0} \Delta_zu
+|z|^2\partial_t^2u = Vu,\quad (z,t) \in \mathbb{R}^N \times \mathbb{R}
\end{equation} where the potential $V$ satisfies either of the following growth
assumptions \begin{align} & |V(z,t)| \leq \frac{f(\rho(z,t))}{\rho(z,t)^2},\
\text{where $f$ satisfies the Dini integrability condition as in (1.3)} \\ &
\text{or when } \notag \\ & |V(z,t)| \leq
C\frac{\psi(z,t)^{\epsilon}}{\rho(z,t)^2},\ \text{for some $\epsilon>0$ with
$\psi$ as in (2.6) and $N$ even.} \notag \end{align} This extends some of the
previous results obtained in [G] for this subfamily of Baouendi-Grushin
operators. As corollaries, we obtain new unique continuation properties for
solutions $u$ to \[ \Delta_{\mathbb{H}} u = Vu \] with certain symmetries as
expressed in (1.6) where $\Delta_{\mathbb{H}}$ corresponds to the sub-Laplacian
on the Heisenberg group $\mathbb{H}^n$.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph