I'm reading an article that has a formula for $\Delta \phi(x)$, where $\phi : \mathbf{R}^2 \rightarrow \mathbf{R}$ and $x \in \mathbf{R}^2$ and $\Delta \phi(x) : \mathbf{R}^2 \rightarrow \mathbf{R}$
From context I think it has to do with the gradient of $\phi$. Specifically I strongly suspect it means $|\nabla \phi(x)|$, but I've never seen $\Delta$ used to mean that. Is that a common practice?
The paper specifically is Transfinite mean value interpolation, bottom of page 17.
$\Delta$ is the Laplace operator defined as
$$\Delta \phi=\frac{\partial^2 \phi}{\partial x^2}+\frac{\partial^2\phi}{\partial y^2}=\langle\nabla,\nabla\rangle\phi$$