Biharmonic equation

（重定向自Biharmonic function）

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

where $\nabla^4$ is the fourth power of the del operator and the square of the laplacian operator $\nabla^2$ (or $\Delta$ ), and it is known as the biharmonic operator or the bilaplacian operator. In summation notation, it can be written in $n$ dimensions as:

单词	Biharmonic function
释义	Biharmonic function 英语百科 Biharmonic equation （重定向自Biharmonic function） 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 $\nabla^4$ is the fourth power of the del operator and the square of the laplacian operator $\nabla^2$ (or $\Delta$ ), and it is known as the biharmonic operator or the bilaplacian operator. In summation notation, it can be written in $n$ dimensions as:
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