%0 Journal Article
%T N维空间中弱导数的一些性质<br>Some Properties of Weak Derivative in N-Dimensional Space
%A 廖玲蓝
%A 邵建鑫
%A 刘红霞
%J Advances in Applied Mathematics
%P 3613-3617
%@ 2324-8009
%D 2021
%I Hans Publishing
%R 10.12677/AAM.2021.1011381
%X 针对某些不满足可导条件的函数，充分运用变分法基本引理、分部积分公式等方法来推广弱导数的性质。从一维的弱导数性质出发，总结证明N维空间中弱导数的一些常用性质，深化分部积分在定积分中的实际应用。通过偏微分方程的学习，N维空间中弱导数的性质更适用于解决高维问题。<br />
For some functions that do not satisfy the differentiable condition, the basic lemma of variational method and partial integral formula are fully used to generalize the properties of weak derivative. Starting from the property of one-dimensional weak derivative, this paper summarizes the property of weak derivative in dimensional space, and deepens the practical application of partial integral in definite integral. Through the learning of partial differential equations, the properties of weak derivatives in N-dimensional space are more suitable for solving higher dimensional problems.
%K 弱导数，分部积分法，变分问题<br>Weak Derivative
%K Integration by Parts
%K Variational Problem
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=46239