Category:Biharmonic Operator
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This category contains results about Biharmonic Operator.
Let $\R^n$ denote the real Cartesian space of $n$ dimensions.
Let $\map U {x_1, x_2, \ldots, x_n}$ be a real-valued function on $\R^n$.
Let $\tuple {\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n}$ be the standard ordered basis on $\R^n$.
Let the partial derivative of $V$ with respect to $x_k$ exist for all $x_k$.
The biharmonic operator on $U$ is defined as:
\(\ds \nabla^4 U\) | \(:=\) | \(\ds \map {\nabla^2} {\nabla^2 U}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {\sum_{k \mathop = 1}^n \dfrac {\partial^2} {\partial x_k^2} } \paren {\sum_{k \mathop = 1}^n \dfrac {\partial^2} {\partial x_k^2} } U\) | Definition of Del Operator |
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