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The geometrical significance of the Laplacian

The geometrical significance of the Laplacian 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The American Journal of Physics American Association of Physics Teachers

The geometrical significance of the Laplacian

The American Journal of Physics , Volume 83 (12) – Dec 1, 2015

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Publisher
American Association of Physics Teachers
Copyright
Copyright © 2015 American Association of Physics Teachers
ISSN
0002-9505
eISSN
1943-2909
DOI
10.1119/1.4935133
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

The American Journal of PhysicsAmerican Association of Physics Teachers

Published: Dec 1, 2015

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