Aside

The geometrical significance of the Laplacian

laplacianDaniel 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

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