Laplacian of the indicator

In potential theory (a branch of mathematics), the Laplacian of the indicator is obtained by letting the Laplace operator work on the indicator function of some domain D. It is a generalisation of the derivative (or "prime function") of the Dirac delta function to higher dimensions; it is non-zero only on the surface of D. It can be viewed as a surface delta prime function, the derivative of a surface delta function (a generalization of the Dirac delta). The Laplacian of the indicator is also analogous to the second derivative of the Heaviside step function in one dimension.

Source: Wikipedia — Laplacian of the indicator (CC BY-SA 4.0)

Laplacian of the indicator

In potential theory (a branch of mathematics), the Laplacian of the indicator is obtained by letting the Laplace operator work on the indicator function of some domain D. It is a generalisation of the derivative (or "prime function") of the Dirac delta function to higher dimensions; it is non-zero only on the surface of D. It can be viewed as a surface delta prime function, the derivative of a surface delta function (a generalization of the Dirac delta). The Laplacian of the indicator is also analogous to the second derivative of the Heaviside step function in one dimension.

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Source: Wikipedia "Laplacian of the indicator" · CC BY-SA 4.0

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