Biharmonic equation
（重定向自Biharmonic）
In mathematics, the biharmonic equation is a fourth-order partial differential equation which arises in areas of continuum mechanics, including linear elasticity theory and the solution of Stokes flows. It is written as
or
or
where 
is the fourth power of the del operator and the square of the laplacian operator 
(or 
), and it is known as the biharmonic operator or the bilaplacian operator. In summation notation, it can be written in 
dimensions as: