Daniel F. Styer
The Laplacian operator can be defined, not only as a differential operator, but also through its averaging properties.
Such a definition lends geometric significance to the operator:
a large Laplacian at a point reflects a “nonconformist” (i.e., different from average) character for the function there. This point of view is used to motivate the wave equation for a drumhead.
…. Read more at scitation.aip.org