Definition 12.1.4 (Quasi-Linear).label We say the function $F(x,\parens{\pd^\al u}_{\abs{\al}\leq k})$ is linear (in $u$) if it is equivalent to
\begin{align*}\sums{}{\abs{\al}=k}a_{\al}(x,\parens{\pd^\be u}_{\abs{\be}\leq k-1})\pd^{\al} u=b(x,\parens{\pd^\be u}_{\abs{\be}\leq k-1})\end{align*}
i.e. $F$ is linear in $k$-th order derivatives. For example $\la u=\abs{\nabla u}^{2}$
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