I'm reading Walter Strauss' PDE book. In section 11.4 he said that the Rayleigh quotient of the following Robin eigenvalue problem
$$ \begin{cases} -\nabla\cdot(p\nabla u) + qu = \lambda mu, & \text{in }D \\ \frac{\partial u}{\partial n} + au = 0, & \text{on }\partial D \end{cases} $$
is
$$ Q = \frac{\int_D p|\nabla w|^2+qw^2 dx + \int_{\partial D} aw^2 dS}{\int_D mw^2 dx}. $$
I'm wondering whether there is a typo. I think the numerator should be
$$ \int_D p|\nabla w|^2+qw^2 dx + \int_{\partial D} \color{red}paw^2 dS. $$
Am I right?