Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial Gaussian bounds for degenerate differential operators II   Let $A = - \sum \partial_k \, c_{kl} \, \partial_l$ be a degenerate sectorial
differential operator with complex bounded mesaurable coefficients. Let $\Omega
\subset \mathds{R}^d$ be open and suppose that $A$ is strongly elliptic on
$\Omega$. Further, let $\chi \in C_{\rm b}^\infty(\mathds{R}^d)$ be such that
an $\varepsilon$-neighbourhood of $\supp \chi$ is contained in $\Omega$. Let
$\nu \in (0,1]$ and suppose that the ${c_{kl}}_{|\Omega} \in
C^{0,\nu}(\Omega)$. Then we prove (H\"older) Gaussian kernel bounds for the
kernel of the operator $u \mapsto \chi \, S_t (\chi \, u)$, where $S$ is the
semigroup generated by $-A$. Moreover, if $\nu = 1$ and the coefficients are
real, then we prove Gaussian bounds for the kernel of the operator $u \mapsto
\chi \, S_t u$ and for the derivatives in the first variable. Finally we show
boundedness on $L_p(\mathds{R}^d)$ of various Riesz transforms.

8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con