Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic operators with unbounded diffusion coefficients perturbed by
  inverse square potentials in $L^p$-spaces   In this paper we give sufficient conditions on $\alpha \geq 0$ and $c\in
\mathbb{R}$ ensuring that the space of test functions
$C_c^\infty(\mathbb{R}^N)$ is a core for the operator $$L_0u=(1+|x|^\alpha
)\Delta u+\frac{c}{|x|^2}u=:Lu+\frac{c}{|x|^2}u,$$ and $L_0$ with suitable
domain generates a quasi-contractive and positivity preserving $C_0$-semigroup
in $L^p(\mathbb{R}^N),\,1<p<\infty$. The proofs are based on some
$L^p$-weighted Hardy's inequality and perturbation techniques.

17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th