Can anyone tell me where the script L in the following snippet comes from? It's not \mathcal{L}:

The mathrsfs package provides \mathscr for script mathematical letters, rather than redefining \mathcal:
\documentclass{article}
\usepackage{mathrsfs}% http://ctan.org/pkg/mathrsfs
\begin{document}
$\mathscr{L}u$
\end{document}

Also consider reading this entry on the TeX FAQ: Better script fonts for maths.