biharmonic equation

Definition. 1.

A real-valued function $V\colon\mathbb{R}^{n}\to\mathbb{R}$ of class (http://planetmath.org/http://planetmath.org/encyclopedia/Cn.html) $C^{4}$, and satisfying the equation

 $\displaystyle\nabla^{4}V=0,$ (1)

also defines a biharmonic function, and (1) is called the biharmonic equation. Biharmonic operator is defined as

 $\nabla^{4}:=\sum_{k=1}^{n}\frac{\partial^{4}}{\partial{x_{k}}^{4}}+2\sum_{k=1}% ^{n-1}\sum_{l=k+1}^{n}\frac{\partial^{4}}{\partial{x_{k}}^{2}\partial{x_{l}}^{% 2}}\cdot$
Title biharmonic equation BiharmonicEquation 2013-03-22 16:03:19 2013-03-22 16:03:19 perucho (2192) perucho (2192) 9 perucho (2192) Definition msc 31B05