Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary regularity of mixed local-nonlocal operators and its
  application   Let $\Omega$ be a bounded $C^2$ domain in $\mathbb{R}^n$ and $u\in
C(\mathbb{R}^n)$ solves \begin{equation*} \begin{aligned} \Delta u + a Iu +
C_0|Du| \geq -K\quad \text{in}\; \Omega, \quad \Delta u + a Iu - C_0|Du|\leq K
\quad \text{in}\; \Omega, \quad u=0\quad \text{in}\; \Omega^c, \end{aligned}
\end{equation*} in viscosity sense, where $0\leq a\leq A_0$, $C_0, K>0$, and
$I$ is a suitable nonlocal operator. We show that $u/\delta$ is in
$C^{\kappa}(\bar \Omega)$ for some $\kappa\in (0,1)$, where $\delta(x)={\rm
dist}(x, \Omega^c)$. Using this result, we also establish that $u\in C^{1,
\gamma}(\bar\Omega)$. Finally, we apply these results to study an
overdetermined problem for mixed local-nonlocal operators.

30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg