Suppose $\Omega$ is a bounded set and connected domain in $\mathbb{R}^n$. Consider the operator $L$ in $\Omega$
$L=a_{ij}(x)D_{ij}u+b_{i}(x)D_{i}u+c(x)u$
For $u \in C^{2}(\Omega)\cap C(\bar{\Omega})$. Se assume that $a_{ij}$, $b_{i}$, and $c$ are continuous and hence bounded $\bar{\Omega}$ and that $L$ ia uniformly elliptic in $\Omega$, that is
$a_{ij}(x)\xi_{i}\xi_{j} \geq \lambda |\xi|^{2}$ for and $x\in \Omega$ and and $\xi \in \mathbb{R}^{n}$. Where $\lambda$ is a positive number. If $\zeta$ denote the sup-norm of $a_{ij}$ and $b_{i}$, that is
$\max_{\Omega}|a_{ij}|+\max_{\Omega}|b_{i}|\leq \zeta$
I have two questions about this introduction :
1) the sup-norm of $a_{ij}$ and $b_{i}$ is the sum of these functions?
2) I did not understand this inequality $\max_{\Omega}|a_{ij}|+\max_{\Omega}|b_{i}|\leq \zeta$.
Thanks for the help!