Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pointwise estimates for degenerate Kolmogorov equations with
  $L^p$-source term   The aim of this paper is to establish new pointwise regularity results for
solutions to degenerate second order partial differential equations with a
Kolmogorov-type operator of the form $$\mathscr{L} :=\sum_{i,j=1}^m
\partial^2_{x_i x_j } +\sum_{i,j=1}^N b_{ij}x_j\partial_{x_i}-\partial_t, $$
where $(x,t) \in \mathbb{R}^{N+1}$, $1 \leq m \le N$ and the matrix
$B:=(b_{ij})_{i,j=1,\ldots,N}$ has real constant entries. In particular, we
show that if the modulus of $L^p$-mean oscillation of $\mathscr{L} u$ at the
origin is Dini, then the origin is a Lebesgue point of continuity in $L^p$
average for the second order derivatives $\partial^2_{x_i x_j} u$,
$i,j=1,\ldots,m$, and the Lie derivative $\left(\sum_{i,j=1}^N
b_{ij}x_j\partial_{x_i}-\partial_t\right)u$. Moreover, we are able to provide a
Taylor-type expansion up to second order with estimate of the rest in $L^p$
norm. The proof is based on decay estimates, which we achieve by contradiction,
blow-up and compactness results.

14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys