Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Hardy Inequality for subelliptic operators with global fundamental
  solution, and an application to Unique Continuation   This is a chapter from PhD Thesis by Stefano Biagi (advisor: prof. A.
Bonfiglioli).
  We overview existing results showing that it is possible to generalize the
classical Hardy's Inequality to more general linear partial differential
operators (PDOs, in the sequel), possibly degenerate-elliptic, of the following
quasi-divergence form $$ \mathcal{L} = \frac{1}{w(x)}\sum_{i =
1}^N\frac{\partial}{\partial x_i}
  \left(\sum_{j = 1}^Nw(x)a_{ij}(x)\frac{\partial}{\partial x_j}\right), \quad
x \in \mathbb{R}^N, $$ where $w \in C^{\infty}(\mathbb{R}^N,\mathbb{R})$ is a
(smooth and) strictly positive function on the whole of $\mathbb{R}^N$ and
$A(x) := \begin{pmatrix}a_{ij}(x) \end{pmatrix}$ is a symmetric and positive
semi-definite $N\times N$ matrix with real $C^{\infty}$ entries. From such a
inequality, it has been derived a result of unique continuation for the
solutions of the equation $$
  -\mathcal{L} u + Vu = 0, $$ where $\mathcal{L}$ is a left-invariant
homogeneous PDO on a homogeneous Lie group $\mathbb{G}$ and $V$ is real-valued
function defined on $\mathbb{G}$ and continuous on $\mathbb{G}\setminus\{0\}$.

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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol