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Biharmonic Operator

The biharmonic operator, also known as the bilaplacian, is the differential operator defined by

del ^4=(del ^2)^2,

where del ^2 is the Laplacian.

In n-dimensional space,

del ^4(1/r)=(3(15-8n+n^2))/(r^5).

See also

Biharmonic Equation, d'Alembertian, Laplacian, von Kármán Equations

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Cite this as:

Weisstein, Eric W. "Biharmonic Operator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BiharmonicOperator.html

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