📝 题目
6.5.5 设 $V,S$ 条件同上题, $u\left( {x,y,z}\right)$ 为调和函数: $\frac{{\partial }^{2}u}{\partial {x}^{2}} + \frac{{\partial }^{2}u}{\partial {y}^{2}} + \frac{{\partial }^{2}u}{\partial {z}^{2}} = 0$ ,且
${\left. u\left( x,y,z\right) \right| }_{S} = 0$ (即函数 $u$ 在边界 $S$ 上取值为零). 证明:
$$ u\left( {x,y,z}\right) \equiv 0\;\le
💡 答案与解析
6. 5.1 (1) ${4\pi }{R}^{3};\;\left( 2\right) \frac{2}{3}\pi {h}^{3};\;\left( 3\right) 1$ (利用变换求重积分).